Index Theory And Operator Algebras

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Index Theory And Operator Algebras

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Author : Jeffrey Stephen Fox
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Index Theory And Operator Algebras written by Jeffrey Stephen Fox and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on $K$-Homology and Index Theory, held in August, 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple $p$-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.

Toeplitz Operators And Index Theory In Several Complex Variables

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Author : Harald Upmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-01-26

Toeplitz Operators And Index Theory In Several Complex Variables written by Harald Upmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-26 with Mathematics categories.

4. 1 Bergman-Toeplitz Operators Over Bounded Domains 242 4. 2 Hardy-Toeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* -Algebras 4. 3 256 4. 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4. 5 Bergman-Toeplitz Operators Over Tubular Domains 278 4. 6 Hardy-Toeplitz Operators Over Polycircular Domains 284 4. 7 Bergman-Toeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* -Algebras 299 4. 9 Actions and Coactions on C* -Algebras 310 4. 10 Hardy-Toeplitz Operators Over K-circular Domains 316 4. 11 Hardy-Toeplitz Operators Over Symmetric Domains 325 4. 12 Bergman-Toeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 K-Theory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*-Algebras K-Theory for 394 5. 4 Index Theory for Symmetric Domains 400 5. 5 Index Theory for Tubular Domains 432 5. 6 Index Theory for Polycircular Domains 455 References 462 Index of Symbols and Notations 471 In trod uction Toeplitz operators on the classical Hardy space (on the I-torus) and the closely related Wiener-Hopf operators (on the half-line) form a central part of operator theory, with many applications e. g. , to function theory on the unit disk and to the theory of integral equations.

Higher Index Theory

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Author : Rufus Willett
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-02

Higher Index Theory written by Rufus Willett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Mathematics categories.

A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.

Index Theory Of Elliptic Operators Foliations And Operator Algebras

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Author : Jerome Kaminker
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Index Theory Of Elliptic Operators Foliations And Operator Algebras written by Jerome Kaminker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.

Modular Theory In Operator Algebras

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Author : Şerban Strǎtilǎ
language : en
Publisher: Cambridge University Press
Release Date : 2020-12-03

Modular Theory In Operator Algebras written by Şerban Strǎtilǎ and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-03 with Mathematics categories.

Discusses the fundamentals and latest developments in operator algebras, focusing on continuous and discrete decomposition of factors of type III.

Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems

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Author : Hermann Schulz-Baldes
language : en
Publisher: Springer Nature
Release Date : 2022-12-31

Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems written by Hermann Schulz-Baldes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-31 with Science categories.

This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.

C Algebras And Operator Theory

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Author : Gerald J. Murphy
language : en
Publisher: Academic Press
Release Date : 2014-06-28

C Algebras And Operator Theory written by Gerald J. Murphy and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

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.

Operator Algebras And Operator Theory

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Author : Liming Ge
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Operator Algebras And Operator Theory written by Liming Ge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

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 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.

Operator Theory Operator Algebras And Their Interactions With Geometry And Topology

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Author : Raul E Curto
language : en
Publisher: Springer Nature
Release Date : 2020-12-12

Operator Theory Operator Algebras And Their Interactions With Geometry And Topology written by Raul E Curto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-12 with Mathematics categories.

This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Fundamentals Of The Theory Of Operator Algebras

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Author : Richard V. Kadison
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Fundamentals Of The Theory Of Operator Algebras written by Richard V. Kadison and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

This second part of this two-volume work presents an introduction to functional analysis and the initial fundamentals of C ]* - and Von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Well supplied with exercises, the text assumes only basic measure theory and topology. The books present the possibility for the design of numerous courses aimed at different audiences.