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Author: Catherine Louise Olsen Publisher: American Mathematical Soc. ISBN: 0821822950 Category : Analytic functions Languages : en Pages : 78
Book Description
The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm and semi-Fredholm theory.
Author: Catherine Louise Olsen Publisher: American Mathematical Soc. ISBN: 0821822950 Category : Analytic functions Languages : en Pages : 78
Book Description
The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm and semi-Fredholm theory.
Author: Șerban Strătilă Publisher: Cambridge University Press ISBN: 1108496849 Category : Mathematics Languages : en Pages : 441
Book Description
The text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.
Author: Jeffrey Stephen Fox Publisher: American Mathematical Soc. ISBN: 0821851527 Category : Mathematics Languages : en Pages : 202
Book Description
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.
Author: Rufus Willett Publisher: Cambridge University Press ISBN: 1108853110 Category : Mathematics Languages : en Pages : 595
Book Description
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Author: John Von Neumann Publisher: World Scientific ISBN: 9789810222017 Category : Mathematics Languages : en Pages : 768
Book Description
After three decades since the first nearly complete edition of John von Neumann's papers, this book is a valuable selection of those papers and excerpts of his books that are most characteristic of his activity, and reveal that of his continuous influence.The results receiving the 1994 Nobel Prizes in economy deeply rooted in Neumann's game theory are only minor traces of his exceptionally broad spectrum of creativity and stimulation.The book is organized by the specific subjects-quantum mechanics, ergodic theory, operator algebra, hydrodynamics, economics, computers, science and society. In addition, one paper which was written in German will be translated and published in English for the first time.The sections are introduced by short explanatory notes with an emphasis on recent developments based on von Neumann's contributions. An overall picture is provided by Ulam's, one of his most intimate partners in thinking, 1958 memorial lecture. Facsimilae and translations of some of his personal letters and a newly completed bibliography based on von Neumann's own careful compilation are added.
Author: Ilwoo Cho Publisher: CRC Press ISBN: 146659019X Category : Mathematics Languages : en Pages : 446
Book Description
This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index theory.
Author: Catherine Louise Olsen
Author: Catherine Louise Olsen
Author: Catherine Louise Olsen
Author: Șerban Strătilă
Author: Hideki Kosaki
Author: Jeffrey Stephen Fox
Author: Allan Sinclair
Author: Rufus Willett
Author: John Von Neumann
Author: Alan L. Carey
Author: Ilwoo Cho