The Mackey Topology on a Von Neumann Algebra - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T01:53:57Z http://mathoverflow.net/feeds/question/71696 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/71696/the-mackey-topology-on-a-von-neumann-algebra The Mackey Topology on a Von Neumann Algebra Andre 2011-07-31T00:30:44Z 2011-08-01T20:18:03Z <p>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 $\mathcal N$?</p> <p>The article below indicates that the answer was unknown at the time of its publication.</p> <p>Aarnes, J. F., <i>On the Mackey-Topology for a Von Neumann Algebra</i>, Math. Scand. 22(1968), 87-107 <a href="http://www.mscand.dk/article.php?id=1864" rel="nofollow">http://www.mscand.dk/article.php?id=1864</a></p>