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Karoubi–Villamayor K-Theory, Weakly Stable C*-Categoroids, and KK-Theory
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T. Kandelaki
Veröffentlicht/Copyright:
4. März 2010
Abstract
The aim of the paper is to give, according to Karoubi–Villamayor K-groups, an interpretation of Kasparov KK-groups. It continues the study of KK-theory by the methods of K-theory, focusing attention on the problem posed and discussed in the author's papers published in 2000 and 2001. But the methods used in those papers are based on the excision property and Morita invariance of algebraic and topological K-theories on the category of C*-algebras, which are not applicable to Karoubi–Villamayor K-theory, since excision holds only for some sub class of short exact sequences of C*-algebras. In this paper we introduce and study a weak stability property of the C*-category Rep(A, B), which is the key to our problem.
Key words and phrases:: Karoubi–Villamayor K-theory of C*-categories; Kasparov KK-theory
Received: 2003-08-04
Revised: 2004-04-02
Published Online: 2010-03-04
Published in Print: 2004-June
© Heldermann Verlag
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Artikel in diesem Heft
- Maximal Subgroups of Some Classes of Semigroups of Binary Relations
- Additive Surjections Preserving Rank One and Applications
- Some Families of Generating Functions for the Bessel and Related Functions
- On the Uniqueness of Solutions of Some Quasi-Variational Inequalities from Control Theory
- The Existence of Solutions for a Semilinear Abstract Dirichlet Problem
- Noncommutative Symplectic Foliation, Bott Connection and Phase Space Reduction
- Karoubi–Villamayor K-Theory, Weakly Stable C*-Categoroids, and KK-Theory
- On Absolutely Nonmeasurable Additive Functions
- On Higher Order Functional Differential Equations with Property A
- On the Behavior of Solutions of Linear Neutral Integrodifferential Equations with Unbounded Delay
- Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Full Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions
- A Sharp Endpoint Estimate for a Multilinear Littlewood–Paley Operator
- On an Initial-Boundary Value Problem for a Fourth Order Composite Equation with Bilaplacian
- An Application of Independent Families of Sets to the Measure Extension Problem
- Oscillation Results for Second Order Self-Adjoint Matrix Differential Systems
