Unitarily invariant norms related to semi-finite factors
Tom 229 / 2015
Studia Mathematica 229 (2015), 13-44
MSC: Primary 46L10; Secondary 46L51.
DOI: 10.4064/sm8019-12-2015
Opublikowany online: 3 December 2015
Streszczenie
Let be a semi-finite factor and let \mathcal J(\mathcal M) be the set of operators T in \mathcal M such that T=ETE for some finite projection E. We obtain a representation theorem for unitarily invariant norms on \mathcal J(\mathcal M) in terms of Ky Fan norms. As an application, we prove that the class of unitarily invariant norms on \mathcal J(\mathcal M) coincides with the class of symmetric gauge norms on a classical abelian algebra, which generalizes von Neumann's classical 1940 result on unitarily invariant norms on M_n(\mathbb C). As another application, Ky Fan's dominance theorem of 1951 is obtained for semi-finite factors.
