This is an announcement for the paper "On C*-algebras which cannot be decomposed into tensor products with factors infinite-dimensional" by Tomasz Kania.

Abstract: We prove that C*-algebras which satisfy a Banach-space property of being a Grothendieck space cannot be decomposed into a tensor product of two infinite-dimensional Banach spaces. By a result of Pfitzner, this class contains all von Neumann algebras and their norm-quotients. We thus strengthen a recent result of Ghasemi who established a similar conclusion for C*-tensor products in the case of SAW*-algebras. In particular, we solve in the negative a problem of Simon Wassermann concerning tensorial decompositions of the Calkin algebra in the category of Banach spaces.

Archive classification: math.OA math.FA

Submitted from: tomasz.marcin.kania@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1412.3621

or

http://arXiv.org/abs/1412.3621