Let ℳ be a semi-finite factor and let 𝓙(ℳ ) be the set of operators T in ℳ such that T = ETE for some finite projection E. We obtain a representation theorem for unitarily invariant norms on 𝓙(ℳ ) in terms of Ky Fan norms. As an application, we prove that the class of unitarily invariant norms on 𝓙(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 Mₙ(ℂ). As another application, Ky Fan's dominance theorem of 1951 is obtained for semi-finite factors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8019-12-2015,
author = {Junsheng Fang and Don Hadwin},
title = {Unitarily invariant norms related to semi-finite factors},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {13-44},
zbl = {06526960},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8019-12-2015}
}
Junsheng Fang; Don Hadwin. Unitarily invariant norms related to semi-finite factors. Studia Mathematica, Tome 231 (2015) pp. 13-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8019-12-2015/