The radius of comparison of the tensor product of a C∗-algebra with C(X)

Abstract

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)⊗B and prove that the dimension-rank ratio satisfies drr(A)=drr(C(X)⊗A). We also give a class of unital AH-algebras A with rc(C(X)⊗A)=rc(A). We further give a class of stably finite exact Z-stable unital C∗-algebras with nonzero radius of comparison.