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Author : Vern Paulsen
Publisher : Cambridge University Press
ISBN 13 : 9780521816694
Total Pages : 316 pages
Book Rating : 4.8/5 (166 download)
Download or read book Completely Bounded Maps and Operator Algebras written by Vern Paulsen and published by Cambridge University Press. This book was released on 2002 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Author : Erling Størmer
Publisher : Springer Science & Business Media
ISBN 13 : 3642343694
Total Pages : 135 pages
Book Rating : 4.6/5 (423 download)
Download or read book Positive Linear Maps of Operator Algebras written by Erling Størmer and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Author : H. Araki
Publisher : Springer Science & Business Media
ISBN 13 : 1461204534
Total Pages : 311 pages
Book Rating : 4.4/5 (612 download)
Download or read book Mappings of Operator Algebras written by H. Araki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of articles contributed by participants at the fourth Ja pan-U.S. Joint Seminar on Operator Algebras. The seminar took place at the University of Pennsylvania from May 23 through May 27, 1988 under the auspices of the Mathematics Department. It was sponsored and supported by the Japan Society for the Promotion of Science and the National Science Foundation (USA). This sponsorship and support is acknowledged with gratitude. The seminar was devoted to discussions and lectures on results and prob lems concerning mappings of operator algebras (C*-and von Neumann alge bras). Among the articles contained in these proceedings, there are papers dealing with actions of groups on C* algebras, completely bounded mappings, index and subfactor theory, and derivations of operator algebras. The seminar was held in honor of the sixtieth birthday of Sh6ichir6 Sakai, one of the great leaders of Functional Analysis for many decades. This vol ume is dedicated to Professor Sakai, on the occasion of that birthday, with the respect and admiration of all the contributors and the participants at the seminar. H. Araki Kyoto, Japan R. Kadison Philadelphia, Pennsylvania, USA Contents Preface.... ..... ....... ........... ...... ......... ................ ...... ............... ... vii On Convex Combinations of Unitary Operators in C*-Algebras UFFE HAAGERUP ......................................................................... .
Author : Huzihiro Araki
Publisher :
ISBN 13 : 9783764334765
Total Pages : 307 pages
Book Rating : 4.3/5 (347 download)
Download or read book Mappings of Operator Algebras written by Huzihiro Araki and published by . This book was released on 1991 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Araki
Publisher :
ISBN 13 : 9781461204541
Total Pages : 324 pages
Book Rating : 4.2/5 (45 download)
Download or read book Mappings of Operator Algebras written by H. Araki and published by . This book was released on 1991-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : KADISON
Publisher : Springer Science & Business Media
ISBN 13 : 1461229685
Total Pages : 599 pages
Book Rating : 4.4/5 (612 download)
Download or read book Fundamentals of the Theory of Operator Algebras written by KADISON and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.
Author : A. Katavolos
Publisher : Springer Science & Business Media
ISBN 13 : 9401155003
Total Pages : 470 pages
Book Rating : 4.4/5 (11 download)
Download or read book Operator Algebras and Applications written by A. Katavolos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field. Among the topics treated are: operator spaces, Hilbert modules, limit algebras, reflexive algebras and subspaces, relations to basis theory, C* algebraic quantum groups, endomorphisms of operator algebras, conditional expectations and projection maps, and applications, particularly to wavelet theory. The volume also features an historical paper offering a new approach to the Pythagoreans' discovery of irrational numbers.
Author : David P. Blecher
Publisher : Clarendon Press
ISBN 13 : 9780198526599
Total Pages : 398 pages
Book Rating : 4.5/5 (265 download)
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.
Author : Bing-Ren Li
Publisher : World Scientific
ISBN 13 : 9789810209414
Total Pages : 758 pages
Book Rating : 4.2/5 (94 download)
Download or read book Introduction to Operator Algebras written by Bing-Ren Li and published by World Scientific. This book was released on 1992 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.
Author : Liming Ge
Publisher : American Mathematical Soc.
ISBN 13 : 0821810936
Total Pages : 389 pages
Book Rating : 4.8/5 (218 download)
Download or read book Operator Algebras and Operator Theory written by Liming Ge and published by American Mathematical Soc.. This book was released on 1998 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered in this title were $C^*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.
Author : K. Schmüdgen
Publisher : Birkhäuser
ISBN 13 : 3034874693
Total Pages : 368 pages
Book Rating : 4.0/5 (348 download)
Download or read book Unbounded Operator Algebras and Representation Theory written by K. Schmüdgen and published by Birkhäuser. This book was released on 2013-11-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: *-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.
Author : M. Amélia Bastos
Publisher : Springer
ISBN 13 : 303480816X
Total Pages : 373 pages
Book Rating : 4.0/5 (348 download)
Download or read book Operator Theory, Operator Algebras and Applications written by M. Amélia Bastos and published by Springer. This book was released on 2014-05-23 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geometry of difference Lax operators).
Author : Peter A. Fillmore and James A. Mingo
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871287
Total Pages : 184 pages
Book Rating : 4.8/5 (712 download)
Download or read book Operator Algebras and Their Applications II written by Peter A. Fillmore and James A. Mingo and published by American Mathematical Soc.. This book was released on 1998-07-28 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of operator algebras, which grew out of von Neumann's work in the 1920s and 30s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality, with significant applications in other areas both within mathematics and in other fields. For this reason, and because of the existence of a strong Canadian school in the subject, the topic was a natural candidate for an emphasis year at The Fields Institute. This volume is the second selection of papers that arose from the seminars and workshops of a year-long program, Operator Algebras and Applications, that took place at The Fields Institute. Topics covered include the classification of amenable C*-algebras, lifting theorems for completely positive maps, and automorphisms of von Neumann algebras of type III.
Author : Igor Frenkel
Publisher : Academic Press
ISBN 13 : 0080874541
Total Pages : 563 pages
Book Rating : 4.0/5 (88 download)
Download or read book Vertex Operator Algebras and the Monster written by Igor Frenkel and published by Academic Press. This book was released on 1989-05-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
Author : Hari Bercovici
Publisher : Springer Science & Business Media
ISBN 13 : 9783764359546
Total Pages : 228 pages
Book Rating : 4.3/5 (595 download)
Download or read book Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics written by Hari Bercovici and published by Springer Science & Business Media. This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Carl Pearcy on the occasion of his 60th birthday, presents recent results in operator theory, nonselfadjoint operator algebras, measure theory and the theory of moments. The articles on these subjects have been contributed by leading area experts, many of whom were associated with Carl Pearcy as students or collaborators.
Author : Kehe Zhu
Publisher : CRC Press
ISBN 13 : 1351467034
Total Pages : 176 pages
Book Rating : 4.3/5 (514 download)
Download or read book An Introduction to Operator Algebras written by Kehe Zhu and published by CRC Press. This book was released on 2018-05-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.
Author : Edward G. Effros
Publisher : American Mathematical Society
ISBN 13 : 1470465051
Total Pages : 358 pages
Book Rating : 4.4/5 (74 download)
Download or read book Theory of Operator Spaces written by Edward G. Effros and published by American Mathematical Society. This book was released on 2022-03-25 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the main results and ideas in the theories of completely bounded maps, operator spaces, and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis to read through the book. The descriptions and discussions of the topics are self-explained. It is appropriate for graduate students new to the subject and the field. The book starts with the basic representation theorems for abstract operator spaces and their mappings, followed by a discussion of tensor products and the analogue of Grothendieck's approximation property. Next, the operator space analogues of the nuclear, integral, and absolutely summing mappings are discussed. In what is perhaps the deepest part of the book, the authors present the remarkable “non-classical” phenomena that occur when one considers local reflexivity and exactness for operator spaces. This is an area of great beauty and depth, and it represents one of the triumphs of the subject. In the final part of the book, the authors consider applications to non-commutative harmonic analysis and non-self-adjoint operator algebra theory. Operator space theory provides a synthesis of Banach space theory with the non-commuting variables of operator algebra theory, and it has led to exciting new approaches in both disciplines. This book is an indispensable introduction to the theory of operator spaces.
