Unitarily invariant norms related to semi-finite factors

@article{JunshengFang2015,
abstract = {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.},
author = {Junsheng Fang, Don Hadwin},
journal = {Studia Mathematica},
keywords = {unitarily invariant norms; semi-finite factors; s-numbers; Ky Fan norms},
language = {eng},
number = {1},
pages = {13-44},
title = {Unitarily invariant norms related to semi-finite factors},
url = {http://eudml.org/doc/286316},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Junsheng Fang
AU - Don Hadwin
TI - Unitarily invariant norms related to semi-finite factors
JO - Studia Mathematica
PY - 2015
VL - 229
IS - 1
SP - 13
EP - 44
AB - 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.
LA - eng
KW - unitarily invariant norms; semi-finite factors; s-numbers; Ky Fan norms
UR - http://eudml.org/doc/286316
ER -