Unitarily invariant norms related to semi-finite factors

• Autorzy: Junsheng Fang , Don Hadwin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L51: Noncommutative measure and integration
• 46L10: General theory of von Neumann algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 229
• Numer: 1
• Strony: 13-44

Daty

wydano

2015

Twórcy

autor

Junsheng Fang

• School of Mathematical Sciences, Dalian University of Technology, Dalian, China, 116024

autor

Don Hadwin

• Department of Mathematics, University of New Hampshire, Durham, NH 03824, U.S.A.

Identyfikatory

DOI

10.4064/sm8019-12-2015