# 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

Contents
Full-Text PDF