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Author : Maurice J. Dupré
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 50,9 Mb
Release : 1979
Category : Mathematics
ISBN : 9780821822227
Author : Karen R. Strung
Publisher : Springer Nature
Page : 322 pages
File Size : 46,9 Mb
Release : 2020-12-15
Category : Mathematics
ISBN : 9783030474652
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 : Richard V. Kadison
Publisher : American Mathematical Soc.
Page : 798 pages
File Size : 43,5 Mb
Release : 1982
Category : Mathematics
ISBN : 0821814419
Author : Robert Doran
Publisher : CRC Press
Page : 447 pages
File Size : 53,9 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781351461788
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 : Dana P. Williams
Publisher : American Mathematical Soc.
Page : 528 pages
File Size : 52,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842423
The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. In addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. In particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. To view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.
Author : Hasan Gündoğan
Publisher : Logos Verlag Berlin GmbH
Page : 172 pages
File Size : 51,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9783832530242
Lie groups and their "derived objects", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on the structure of finite-dimensional Lie algebras, the classification and structure theory of infinite-dimensional Lie algebras has become an interesting and fairly vast field of interest. This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.
Author : Bogdan Bojarski,Alexander S. Mishchenko,Evgenij V. Troitsky,Andrzej Weber
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 52,9 Mb
Release : 2006-11-09
Category : Mathematics
ISBN : 9783764376871
This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
Author : Thomas Karl Müller
Publisher : Unknown
Page : 100 pages
File Size : 48,5 Mb
Release : 1990
Category : C*-algebras
ISBN : UCR:31210012616494
Author : J. M.G. Fell,R. S. Doran
Publisher : Academic Press
Page : 771 pages
File Size : 49,7 Mb
Release : 1988-04-15
Category : Mathematics
ISBN : 9780080874449
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Author : Maurice J. Dupré,R. M. Gillette
Publisher : Pitman Advanced Publishing Program
Page : 132 pages
File Size : 53,5 Mb
Release : 1983
Category : Mathematics
ISBN : UCAL:B4405660
Author : Robert S. Doran
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 49,5 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821851272
This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S. Muhly (which will be published in a CBMS Regional Conference Series volume), twenty-eight lectures were delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, over one hundred problems and questions are scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.
Author : Dale Husemöller,Michael JOACHIM,Branislav Jurco,Martin Schottenloher
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,8 Mb
Release : 2007-12-18
Category : Mathematics
ISBN : 9783540749554
Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.
Author : Anonim
Publisher : Unknown
Page : 716 pages
File Size : 54,7 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015046576693
Author : Dumitru Gaspar,Israel Gohberg,Dan Timotin,Florian H. Vasilescu,Laszlo Zsido
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 50,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373146
This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.
Author : Iain Raeburn,Dana P. Williams
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 43,8 Mb
Release : 1998
Category : C*-algebras
ISBN : 9780821808603
A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR
