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5 votes
0 answers
254 views

Examples of non-proper conditional expectations onto von Neumann subalgebras of $II_{1}$ factors

Denote by $M$ be a type $II_{1}$ factor with trace $\tau$, and $1\in N\subseteq M$ a von Neumann subalgebra. What are some examples of such inclusions for which the normal conditional expectation $\...
Jon Bannon's user avatar
  • 7,057
11 votes
4 answers
2k views

What kind of completion is this?

Let $X$ be a compact Hausdorff space, and $C(X)$ the unital commutative C*-algebra of continuous functions on it. The double Banach dual $C(X)^{**}$ is a commutative von Neumann algebra and hence has ...
Chris Heunen's user avatar
  • 3,937
8 votes
1 answer
426 views

Is $L(\mathbb{Z}*\mathbb{Z}_{2})$ a free group factor?

This is a reference request for something that is likely to be well-known to operator algebraists. I will not, therefore, include the technical definition of free product of finite von Neumann ...
Jon Bannon's user avatar
  • 7,057
7 votes
1 answer
990 views

Subfactor theory and Hilbert von Neumann Algebras

There seem to be intimate connections between the different definitions of von Neumann module. The two that I'm aware of are Hilbert von Neumann modules and correspondences (in the sense of Connes). I ...
Ollie's user avatar
  • 1,411