K Theory for Operator Algebras

[Dg 2] R. Douglas, Ext and index theory, Operator Algebras and Applications (ed. R. V. Kadison), Proc. Symp. Pure Math. 38, Amer. Math. Soc., Providence, 1981. [Ef 1] E. Effros, Aspects of non-commutative geometry, ...

K Theory for Operator Algebras

K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

More Books:

K-Theory and Operator Algebras
Language: en
Pages: 194
Authors: B.B. Morrel, I.M. Singer
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

Books about K-Theory and Operator Algebras
Index Theory and Operator Algebras
Language: en
Pages: 190
Authors: Jeffrey Stephen Fox, Peter Haskell
Categories: Mathematics
Type: BOOK - Published: 1993 - Publisher: American Mathematical Soc.

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
Operator Algebras and $K$-Theory
Language: en
Pages: 204
Authors: Ronald G. Douglas, Claude Schochet
Categories: Mathematics
Type: BOOK - Published: 1982 - Publisher: American Mathematical Soc.

Books about Operator Algebras and $K$-Theory
Index Theory of Elliptic Operators, Foliations, and Operator Algebras
Language: en
Pages: 322
Authors: Jerome Kaminker, Kenneth C. Millett, American Mathematical Society
Categories: Mathematics
Type: BOOK - Published: 1988 - Publisher: American Mathematical Soc.

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
Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology
Language: en
Pages: 256
Authors: Professor of Mathematics David E Evans, David E. Evans, Masamichi Takesaki, N. J. Hitchin
Categories: Mathematics
Type: BOOK - Published: 1988 - Publisher: Cambridge University Press

These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.