On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional

Kania, Tomasz (2015) On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional. The Quarterly Journal of Mathematics, 66 (4). pp. 1063-1068. ISSN 0033-5606

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Abstract

We prove that C*-algebras which, as Banach spaces, are Grothendieck cannot be decomposed into a tensor product of two infinite-dimensional C*-algebras. By a result of Pfitzner, this class contains all von Neumann algebras and their norm-quotients. We thus complement a recent result of Ghasemi who established a similar conclusion for the class of SAW*-algebras.