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.

Item Type:
Journal Article
Journal or Publication Title:
The Quarterly Journal of Mathematics
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
75409
Deposited By:
Deposited On:
09 Sep 2015 06:32
Refereed?:
Yes
Published?:
Published
Last Modified:
26 Nov 2020 03:12