Journal of Operator Theory

Volume 86, Issue 1, Summer 2021 pp. 31-50.

The radius of comparison of the tensor product of a $C^*$-algebra with $C (X)$

Authors: Mohammad B. Asadi (1), M. Ali Asadi-Vasfi (2)
Author institution: (1) School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, 14155-6619, Iran
(2) School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, 14155-6619, Iran

Summary: Let $X$ be a compact metric space, let $A$ be a unital AH-algebra with large matrix sizes, and let $B$ be a stably finite unital $C^*$-algebra. Then we give a lower bound for the radius of comparison of $C(X) \otimes B$ and prove that the dimension-rank ratio satisfies $\mathrm{drr} (A) = \mathrm{drr} (C(X)\otimes A )$. We also give a class of unital AH-algebras $A$ with $\mathrm{rc} (C(X) \otimes A ) = \mathrm{rc} (A)$. We further give a class of stably finite exact $\mathcal{Z}$-stable unital $C^*$-algebras with nonzero radius of comparison.

DOI: http://dx.doi.org/10.7900/jot.2020jan20.2267
Keywords: covering dimension, Cuntz semigroup, dimension-rank ratio, radius of comparison

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