Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles

Author: J. M.G. Fell

Publisher: Academic Press

Published: 1988-05-01

Total Pages: 755

ISBN-13: 0080874452

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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.

Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles

Author: J. M.G. Fell

Publisher: Academic Press

Published: 1988-04-15

Total Pages: 771

ISBN-13: 0080874444

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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.

Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles

Author: J. M.G. Fell

Publisher: Academic Press

Published: 1988-05-12

Total Pages: 752

ISBN-13: 9780122527227

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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.

Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles

Author: J. M.G. Fell

Publisher: Academic Press

Published: 1988-04-11

Total Pages: 746

ISBN-13: 9780122527210

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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.

Crossed Products of $C^*$-Algebras
Crossed Products of $C^*$-Algebras

Author: Dana P. Williams

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 546

ISBN-13: 0821842420

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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.

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

Author: Theodore W. Palmer

Publisher: Cambridge University Press

Published: 1994-03-25

Total Pages: 820

ISBN-13: 9780521366373

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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.

Continuous Bounded Cohomology of Locally Compact Groups
Continuous Bounded Cohomology of Locally Compact Groups

Author: Nicolas Monod

Publisher: Springer

Published: 2003-07-01

Total Pages: 219

ISBN-13: 3540449620

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Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.

An Invitation to Quantum Groups and Duality
An Invitation to Quantum Groups and Duality

Author: Thomas Timmermann

Publisher: European Mathematical Society

Published: 2008

Total Pages: 436

ISBN-13: 9783037190432

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This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.