The Similarity Problem for Z-stable C*-algebras

TL;DR

This paper proves that certain tensor products of unital C*-algebras, especially those involving the Jiang-Su algebra, possess Kadison's similarity property, advancing understanding of their structural similarities.

Contribution

It establishes that tensor products with nuclear algebras admitting a unital *-homomorphism from the Jiang-Su algebra have Kadison's similarity property, extending previous results.

Findings

Tensor product of nuclear C*-algebras with Jiang-Su algebra admits Kadison's similarity property

Unital C*-algebras absorbing the Jiang-Su algebra tensorially also have this property

Advances the understanding of the similarity problem in the context of Z-stable C*-algebras

Abstract

We show that the tensor product of two unital C*-algebras, one of which is nuclear and admits a unital *-homomorphism from (the building blocks of) the Jiang-Su algebra, has Kadison's similarity property. As a consequence, we obtain that a unital C*-algebra which absorbs the Jiang-Su algebra tensorially also has this property.