Journal of Operator Theory
Volume 76, Issue 2, Fall 2016 pp. 271-283.
Weak* tensor products for von Neumann algebras
Authors:
Matthew Wiersma
Author institution:Department of Mathematical and Statistical
Sciences, University of Alberta, Edmonton, AB, Canada, N2L 1W5
Summary: The category of $C^*$-algebras is blessed with many
different tensor products. In contrast, virtually the only tensor product
ever used in the category of von Neumann algebras is the normal spatial
tensor product. In this paper, we propose a definition of what a generic
tensor product in this category should be. We call these
{\it weak* tensor products}. A complete characterization for an analogue
of nuclearity for weak* tensor products is given and we construct
$2^{\mathfrak c}$ nonequivalent weak* tensor product completions of
$L^\infty(\mathbb R)\odot L^\infty(\mathbb R)$.
DOI: http://dx.doi.org/10.7900/jot.2015jul24.2103
Keywords: von Neumann algebras, tensor products
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