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Author :
Publisher : Elsevier
ISBN 13 : 0080528341
Total Pages : 441 pages
Book Rating : 4.0/5 (85 download)
Download or read book General Theory of C*-Algebras written by and published by Elsevier. This book was released on 2001-07-11 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Theory of C*-Algebras
Author : Gerald J. Murphy
Publisher : Academic Press
ISBN 13 : 0080924964
Total Pages : 297 pages
Book Rating : 4.0/5 (89 download)
Download or read book C*-Algebras and Operator Theory written by Gerald J. Murphy and published by Academic Press. This book was released on 2014-06-28 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
Author : Corneliu Constantinescu
Publisher :
ISBN 13 :
Total Pages : 417 pages
Book Rating : 4.:/5 (648 download)
Download or read book General Theory of C*-algebras written by Corneliu Constantinescu and published by . This book was released on 2001 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Karen R. Strung
Publisher : Springer Nature
ISBN 13 : 3030474658
Total Pages : 322 pages
Book Rating : 4.0/5 (34 download)
Download or read book An Introduction to C*-Algebras and the Classification Program written by Karen R. Strung and published by Springer Nature. This book was released on 2020-12-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
Author : M. Rørdam
Publisher : Cambridge University Press
ISBN 13 : 9780521789448
Total Pages : 260 pages
Book Rating : 4.7/5 (894 download)
Download or read book An Introduction to K-Theory for C*-Algebras written by M. Rørdam and published by Cambridge University Press. This book was released on 2000-07-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Author : Theodore W. Palmer
Publisher : Cambridge University Press
ISBN 13 : 9780521366373
Total Pages : 820 pages
Book Rating : 4.3/5 (663 download)
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.
Author : Charles Earl Rickart
Publisher : Krieger Publishing Company
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.3/5 (97 download)
Download or read book General Theory of Banach Algebras written by Charles Earl Rickart and published by Krieger Publishing Company. This book was released on 1974 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shoichiro Sakai
Publisher : Springer Science & Business Media
ISBN 13 : 3642619932
Total Pages : 271 pages
Book Rating : 4.6/5 (426 download)
Download or read book C*-Algebras and W*-Algebras written by Shoichiro Sakai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." Mathematical Reviews
Author : Ilijas Farah
Publisher : Springer Nature
ISBN 13 : 3030270939
Total Pages : 517 pages
Book Rating : 4.0/5 (32 download)
Download or read book Combinatorial Set Theory of C*-algebras written by Ilijas Farah and published by Springer Nature. This book was released on 2019-12-24 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.
Author : Bruce Blackadar
Publisher : Taylor & Francis
ISBN 13 : 9783540284864
Total Pages : 552 pages
Book Rating : 4.2/5 (848 download)
Download or read book Operator Algebras written by Bruce Blackadar and published by Taylor & Francis. This book was released on 2006 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.
Author : W. Arveson
Publisher : Springer Science & Business Media
ISBN 13 : 1461263719
Total Pages : 117 pages
Book Rating : 4.4/5 (612 download)
Download or read book An Invitation to C*-Algebras written by W. Arveson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2.
Author : Robert Doran
Publisher : CRC Press
ISBN 13 : 1351461788
Total Pages : 447 pages
Book Rating : 4.3/5 (514 download)
Download or read book Characterizations of C* Algebras written by Robert Doran and published by CRC Press. This book was released on 2018-05-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified, in-depth discussion of the now classical Gelfand-Naimark theorems, thiscomprehensive text assesses the current status of modern analysis regarding both Banachand C*-algebras.Characterizations of C*-Algebras: The Gelfand-Naimark Theorems focuses on general theoryand basic properties in accordance with readers' needs ... provides complete proofs of theGelfand-Naimark theorems as well as refinements and extensions of the original axioms. . . gives applications of the theorems to topology, harmonic analysis. operator theory.group representations, and other topics ... treats Hermitian and symmetric *-algebras.algebras with and without identity, and algebras with arbitrary (possibly discontinuous)involutions . . . includes some 300 end-of-chapter exercises . . . offers appendices on functionalanalysis and Banach algebras ... and contains numerous examples and over 400 referencesthat illustrate important concepts and encourage further research.Characterizations of C*-Algebras: The Gelfand-Naimark Theorems is an ideal text for graduatestudents taking such courses as The Theory of Banach Algebras and C*-Algebras: inaddition , it makes an outstanding reference for physicists, research mathematicians in analysis,and applied scientists using C*-algebras in such areas as statistical mechanics, quantumtheory. and physical chemistry.
Author : Kirill C. H. Mackenzie
Publisher : Cambridge University Press
ISBN 13 : 0521499283
Total Pages : 540 pages
Book Rating : 4.5/5 (214 download)
Download or read book General Theory of Lie Groupoids and Lie Algebroids written by Kirill C. H. Mackenzie and published by Cambridge University Press. This book was released on 2005-06-09 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.
Author : Theodore W. Palmer
Publisher : Cambridge University Press
ISBN 13 : 9780521366380
Total Pages : 846 pages
Book Rating : 4.3/5 (663 download)
Download or read book Banach Algebras and the General Theory of *-Algebras: Volume 2, *-Algebras written by Theodore W. Palmer and published by Cambridge University Press. This book was released on 1994 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second of two volumes gives a modern exposition of the theory of Banach algebras.
Author : Brian Hall
Publisher : Springer
ISBN 13 : 3319134671
Total Pages : 452 pages
Book Rating : 4.3/5 (191 download)
Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Author : Kenneth R. Davidson
Publisher : American Mathematical Society, Fields Institute
ISBN 13 : 1470475081
Total Pages : 325 pages
Book Rating : 4.4/5 (74 download)
Download or read book C*-Algebras by Example written by Kenneth R. Davidson and published by American Mathematical Society, Fields Institute. This book was released on 2023-10-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty years has been based on a careful study of these special classes. While there are many books on C*-algebras and operator algebras available, this is the first one to attempt to explain the real examples that researchers use to test their hypotheses. Topics include AF algebras, Bunce–Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, group C*-algebras, discrete crossed products, abelian C*-algebras (spectral theory and approximate unitary equivalence) and extensions. It also introduces many modern concepts and results in the subject such as real rank zero algebras, topological stable rank, quasidiagonality, and various new constructions. These notes were compiled during the author's participation in the special year on C*-algebras at The Fields Institute for Research in Mathematical Sciences during the 1994–1995 academic year. The field of C*-algebras touches upon many other areas of mathematics such as group representations, dynamical systems, physics, $K$-theory, and topology. The variety of examples offered in this text expose the student to many of these connections. Graduate students with a solid course in functional analysis should be able to read this book. This should prepare them to read much of the current literature. This book is reasonably self-contained, and the author has provided results from other areas when necessary.
Author : Brian C. Hall
Publisher : Springer Science & Business Media
ISBN 13 : 9780387401225
Total Pages : 376 pages
Book Rating : 4.4/5 (12 download)
Download or read book Lie Groups, Lie Algebras, and Representations written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2003-08-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.
