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Exponential length and traces

Published online by Cambridge University Press:  14 November 2011

N.Christopher Phillips
N.Christopher Phillips
Affiliation:
Department of Mathematics, University of Oregon, Eugene OR 97403-1222, U.S.A.(current address); and Department of Mathematics, University of Georgia, Athens GA 30602, U.S.A.
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Abstract

We define a quantity called the reduced C* exponential rank rcel (A) of a C*-algebra A, which satisfies rcel (A) ≦ cel (A). We show that rcel (A) = ∞ whenever A has two distinct normalised traces which agree on K0(A), and we prove a partial converse. This gives some understanding of why cel (A) = π cer (A) for some C*-algebras A but not for others. We also characterise rcel (A) as the supremum of the rectifiable distances from unitaries in the identity component of the unitary group to the commutator subgroup of this component.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 1 , 1995 , pp. 13 - 29
Copyright
Copyright © Royal Society of Edinburgh 1995

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