On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional
Operator Algebras
2016-10-26 v3 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1412.3621,
title = {On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional},
author = {Tomasz Kania},
journal= {arXiv preprint arXiv:1412.3621},
year = {2016}
}
Comments
6 pp., to appear in The Quarterly Journal of Mathematics