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    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The definitive publisher-authenticated version Kania, Tomasz On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional Quarterly Journal of Mathematics 2015 66, 4 1063-1068 is available online at: http://qjmath.oxfordjournals.org/cgi/content/abstract/66/4/1063

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

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  • Tomasz Kania
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<mark>Journal publication date</mark>31/12/2015
<mark>Journal</mark>The Quarterly Journal of Mathematics
Issue number4
Volume66
Number of pages6
Pages (from-to)1063-1068
Publication StatusPublished
Early online date23/09/15
<mark>Original language</mark>English

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.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The definitive publisher-authenticated version Kania, Tomasz On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional Quarterly Journal of Mathematics 2015 66, 4 1063-1068 is available online at: http://qjmath.oxfordjournals.org/cgi/content/abstract/66/4/1063