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

Jonathan Rosenberg ()
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Jonathan Rosenberg: University of Maryland

Chapter IV.3 in Handbook of K-Theory, 2005, pp 843-874 from Springer

Abstract: 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.

Keywords: Exact Sequence; Operator Algebra; Toeplitz Operator; Banach Algebra; Inductive Limit (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/978-3-540-27855-9_16

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