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The space of $\mathcal A$-Hilbert Schmidt Operators.

Let $\mathcal A$ be a finite von Neumann algebra with finite trace $\tau$ and let $l^2(\mathcal A)$ be the Hilbert space completion of $\mathcal A$ with respect to the inner product induced by $\tau$, ...
5 votes
0 answers
207 views

Foliations, von Neumann algebras and measurability

In the excellent book Noncommutative Geometry by Alain Connes much of the first chapter is devoted to foliations. At the end of the first chapter the author discusses index theory on measured ...
21 votes
1 answer
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Is Dependent Choice all we really need?

http://en.wikipedia.org/wiki/Axiom_of_dependent_choice Is DC sufficient for the understanding of objects that are countable in some suitable sense? For example, is DC sufficient for the full ...