Uniform Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821840498
Total Pages : 292 pages
Book Rating : 4.8/5 (44 download)

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Book Synopsis Uniform Algebras by : Theodore W. Gamelin

Download or read book Uniform Algebras written by Theodore W. Gamelin and published by American Mathematical Soc.. This book was released on 2005 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: ``The functional-analytic approach to uniform algebras is inextricably interwoven with the theory of analytic functions ... [T]he concepts and techniques introduced to deal with these problems [of uniform algebras], such as ``peak points'' and ``parts,'' provide new insights into the classical theory of approximation by analytic functions. In some cases, elegant proofs of old results are obtained by abstract methods. The new concepts also lead to new problems in classical function theory, which serve to enliven and refresh that subject. In short, the relation between functional analysis and the analytic theory is both fascinating and complex, and it serves to enrich and deepen each of the respective disciplines.'' This volume includes a Bibliography, List of Special Symbols, and an Index. Each of the chapters is followed by notes and numerous exercises.

Shift-invariant Uniform Algebras on Groups

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Publisher : Springer Science & Business Media
ISBN 13 : 3764376058
Total Pages : 287 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Shift-invariant Uniform Algebras on Groups by : Suren A. Grigoryan

Download or read book Shift-invariant Uniform Algebras on Groups written by Suren A. Grigoryan and published by Springer Science & Business Media. This book was released on 2006-08-08 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on the theory of shift-invariant algebras is the first monograph devoted entirely to an outgrowth of the established theory of generalized analytic functions on compact groups. Associated subalgebras of almost periodic functions of real variables and of bonded analytic functions on the unit disc are carried along within the general framework.

Topological Uniform Structures

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Publisher : Courier Dover Publications
ISBN 13 : 9780486658087
Total Pages : 398 pages
Book Rating : 4.6/5 (58 download)

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Book Synopsis Topological Uniform Structures by : Warren Page

Download or read book Topological Uniform Structures written by Warren Page and published by Courier Dover Publications. This book was released on 1988 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exceptionally smooth, clear, detailed examination of uniform spaces, topological groups, topological vector spaces, topological algebras and abstract harmonic analysis. Also, topological vector-valued measure spaces as well as numerous problems and examples. For advanced undergraduates and beginning graduate students. Bibliography. Index.

Real Function Algebras

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Publisher : CRC Press
ISBN 13 : 1000105636
Total Pages : 201 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Real Function Algebras by : S.H. Kulkarni

Download or read book Real Function Algebras written by S.H. Kulkarni and published by CRC Press. This book was released on 2020-08-26 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.

Operator Algebras and Their Modules

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Publisher : Clarendon Press
ISBN 13 : 0198526598
Total Pages : 398 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Operator Algebras and Their Modules by : David P. Blecher

Download or read book Operator Algebras and Their Modules written by David P. Blecher and published by Clarendon Press. This book was released on 2004 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward noncommutative' or quantized' phenomena. In functional analysis, this has appeared notably under the name of operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, Non-selfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important non-commutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.

A Course in Commutative Banach Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 0387724761
Total Pages : 362 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis A Course in Commutative Banach Algebras by : Eberhard Kaniuth

Download or read book A Course in Commutative Banach Algebras written by Eberhard Kaniuth and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen’s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.

Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras

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Publisher : Cambridge University Press
ISBN 13 : 9780521366373
Total Pages : 820 pages
Book Rating : 4.3/5 (663 download)

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Book Synopsis Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras by : Theodore W. Palmer

Download or read book Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras written by Theodore W. Palmer and published by Cambridge University Press. This book was released on 1994-03-25 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.

Banach Function Algebras, Arens Regularity, and BSE Norms

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Publisher : Springer Nature
ISBN 13 : 3031445325
Total Pages : 452 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Banach Function Algebras, Arens Regularity, and BSE Norms by : Harold Garth Dales

Download or read book Banach Function Algebras, Arens Regularity, and BSE Norms written by Harold Garth Dales and published by Springer Nature. This book was released on with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complete Normed Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 3642656692
Total Pages : 312 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Complete Normed Algebras by : Frank F. Bonsall

Download or read book Complete Normed Algebras written by Frank F. Bonsall and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.

Deformation Theory of Algebras and Structures and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9400930577
Total Pages : 1024 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Deformation Theory of Algebras and Structures and Applications by : Michiel Hazewinkel

Download or read book Deformation Theory of Algebras and Structures and Applications written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).

Big-Planes, Boundaries and Function Algebras

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Publisher : Elsevier
ISBN 13 : 0080872832
Total Pages : 313 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Big-Planes, Boundaries and Function Algebras by : T.V. Tonev

Download or read book Big-Planes, Boundaries and Function Algebras written by T.V. Tonev and published by Elsevier. This book was released on 1992-03-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treated in this volume are selected topics in analytic &Ggr;-almost-periodic functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-periodic structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.

Function Spaces

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Publisher : American Mathematical Soc.
ISBN 13 : 0821840614
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Function Spaces by : Krzysztof Jarosz

Download or read book Function Spaces written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2007 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.

Introduction to Banach Algebras, Operators, and Harmonic Analysis

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Publisher : Cambridge University Press
ISBN 13 : 9780521535847
Total Pages : 338 pages
Book Rating : 4.5/5 (358 download)

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Book Synopsis Introduction to Banach Algebras, Operators, and Harmonic Analysis by : H. Garth Dales

Download or read book Introduction to Banach Algebras, Operators, and Harmonic Analysis written by H. Garth Dales and published by Cambridge University Press. This book was released on 2003-11-13 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents

Perturbation of Banach Algebras

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Publisher : Springer
ISBN 13 : 3540393706
Total Pages : 123 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Perturbation of Banach Algebras by : Krzysztof Jarosz

Download or read book Perturbation of Banach Algebras written by Krzysztof Jarosz and published by Springer. This book was released on 2006-11-14 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Natural Function Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461380707
Total Pages : 252 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Natural Function Algebras by : Charles E. Rickart

Download or read book Natural Function Algebras written by Charles E. Rickart and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func tion algebras".

Triangular Algebras and Ideals of Nest Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 0821804057
Total Pages : 65 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Triangular Algebras and Ideals of Nest Algebras by : John Lindsay Orr

Download or read book Triangular Algebras and Ideals of Nest Algebras written by John Lindsay Orr and published by American Mathematical Soc.. This book was released on 1995 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Immersive environments such as virtual reality technology makes possible can respond to their audiences, so that each person's experience of the environment is unique. This volume brings together 11 essays along with artists' projects produced at the Banff Centre for the Arts in Canada to explore issues raised by the creation of virtual environments. The essays approach the social and cultural implications of cyberspace from the perspective of cultural studies, communications, art history, art criticism, English, and women's studies; while artists who created nine virtual worlds at the Banff Centre discuss what they have tried to accomplish in both theoretical and technical terms. With 64 illustrations, including 18 color plates. Annotation copyright by Book News, Inc., Portland, OR

The Theory of Uniform Algebras

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Publisher :
ISBN 13 :
Total Pages : 536 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis The Theory of Uniform Algebras by : Edgar Lee Stout

Download or read book The Theory of Uniform Algebras written by Edgar Lee Stout and published by . This book was released on 1971 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: