A criterion for splitting 𝐶*-algebras in tensor products

Zsidó, László

doi:10.1090/S0002-9939-99-05269-7

A criterion for splitting $C^\ast$-algebras in tensor products
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Proc. Amer. Math. Soc. 128 (2000), 2001-2006 Request permission

Abstract:

The goal of the paper is to prove the following theorem: if $A$,$D$ are unital $C^{*}$-algebras, $A$ simple and nuclear, then any $C^{*}$-subalgebra of the $C^{*}$-tensor product of $A$ and $D$, which contains the tensor product of $A$ with the scalar multiples of the unit of $D$, splits in the $C^{*}$-tensor product of $A$ with some $C^{*}$-subalgebra of $D$.

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