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Reduction of Exponential Rank in Direct Limits of C*-Algebras

Published online by Cambridge University Press:  20 November 2018

N. Christopher Phillips
N. Christopher Phillips*
Affiliation:
Department of Mathematics, University of Oregon Eugene, Oregon 97403-1222U.S.A.
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Abstract

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We prove the following result. Let A be a direct limit of direct sums of C*-algebras of the form C(X) ⊗ Mn, with the spaces X being compact metric. Suppose that there is a finite upper bound on the dimensions of the spaces involved, and suppose that A is simple. Then the C* exponential rank of A is at most 1 + ε, that is, every element of the identity component of the unitary group of A is a limit of exponentials. This is true regardless of whether the real rank of A is 0 or 1.

Keywords

46L05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 4 , 01 August 1994 , pp. 818 - 853
Copyright
Copyright © Canadian Mathematical Society 1994

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