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Comparison Between Algebraic and Topological K-Theory for Banach Algebras and C*-Algebras

In: Handbook of K-Theory

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  • Jonathan Rosenberg

    (University of Maryland)

Abstract

For a Banach algebra, one can define two kinds of K-theory: topological K-theory, which satisfies Bott periodicity, and algebraic K-theory, which usually does not. It was discovered, starting in the early 80’s, that the “comparison map” from algebraic to topological K-theory is a surprisingly rich object. About the same time, it was also found that the algebraic (as opposed to topological) K-theory of operator algebras does have some direct applications in operator theory. This article will summarize what is known about these applications and the comparison map.

Suggested Citation

  • Jonathan Rosenberg, 2005. "Comparison Between Algebraic and Topological K-Theory for Banach Algebras and C*-Algebras," Springer Books, in: Eric M. Friedlander & Daniel R. Grayson (ed.), Handbook of K-Theory, chapter 0, pages 843-874, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27855-9_16
    DOI: 10.1007/978-3-540-27855-9_16
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