22
$\begingroup$

Every von Neumann algebra $\mathcal M$ is the dual of a unique Banach space $\mathcal M_* $. The Mackey topology on $\mathcal M$ is the topology of uniform convergence on weakly compact subsets of $\mathcal M_*$. Is it known whether given a von Neumann subalgebra $\mathcal N \subseteq \mathcal M$, the Mackey topology on $\mathcal M$ restricts to the Mackey topology on $\mathcal N$?

The article below indicates that the answer was unknown at the time of its publication.

Aarnes, J. F., On the Mackey-Topology for a Von Neumann Algebra, Math. Scand. 22(1968), 87-107 http://www.mscand.dk/article.php?id=1864

$\endgroup$

1 Answer 1

5
$\begingroup$

This recent paper says that it is still unknown: https://arxiv.org/abs/1411.1890.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.