Analyticity, Uniform Averaging and K-Theory

Paul S. Muhly, Chaoxin Qiu and Jingbo Xia
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Paul S. Muhly: University of Iowa, Department of Mathematics
Chaoxin Qiu: University of Nevada at Reno, Department of Mathematics
Jingbo Xia: State University of New York, Department of Mathematics

A chapter in Algebraic Methods in Operator Theory, 1994, pp 328-349 from Springer

Abstract: Abstract Let (A, R, α) be a C*-dynamical systerr, let H∞(α) be the subalgebra of A consisting of those a in A such that the Arveson spectrum of a is contained in [0, ∞), and let Aα be the fixed point subalgebra of A. In this note we investigate conditions for the existence of an R-invariant conditional expectation from A onto Aα and we show that when such an expectation exists, then the K-theory of H∞(α) is isomorphic to that of Aα. We show by example that if no such expectation exists, then the K-theories may be different.

Keywords: Automorphism Group; Operator Algebra; Uniform Average; Poisson Kernel; Maximal Ideal Space (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_32

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DOI: 10.1007/978-1-4612-0255-4_32

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