Journal of Operator Theory

Volume 47, Issue 1, Winter 2002 pp. 117-130.

Real rank and exponential length of tensor products with

$\Cal O_\infty$

Authors: N. Christopher Phillips
Author institution: Department of Mathematics, University of Oregon, Eugene, OR 97403--1222, USA

Summary: Let

$D$ be any \ca. We prove that

$\Cal O_\infty \otimes D$ has real rank at most

$1$ , exponential length at most

$2 \pi$ , exponential rank at most

$2 + \varepsilon$ , and

$C^*$ projective length at most

$\pi$ . The algebra

$\Cal O_\infty$ can be replaced with any separable nuclear purely infinite simple \ca.

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