Analyticity, Uniform Averaging and K-Theory

Paul S Muhly; Chaoxin Qiu; Jingbo Xia

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

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Book chapter

Analyticity, Uniform Averaging and K-Theory

Paul S Muhly, Chaoxin Qiu and Jingbo Xia

Algebraic Methods in Operator Theory, pp.328-349

Birkhäuser Boston

1994

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

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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.

Operator Algebra

Automorphism Group

Maximal Ideal Space

Uniform Average

Poisson Kernel

Details

Title: Subtitle: Analyticity, Uniform Averaging and K-Theory
Creators: Paul S Muhly
Chaoxin Qiu
Jingbo Xia
Resource Type: Book chapter
Publication Details: Algebraic Methods in Operator Theory, pp.328-349
DOI: 10.1007/978-1-4612-0255-4_32
Publisher: Birkhäuser Boston; Boston, MA
Language: English
Date published: 1994
Academic Unit: Statistics and Actuarial Science; Mathematics
Record Identifier: 9984083221302771

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