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Unitarily invariant norms related to semi-finite factors

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Fang J., Hadwin D.

Studia Mathematica

2015

tom 229

nr 1

13-44

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.

Ograniczanie wyników

1 Studia Mathematica

1 Fang J.

1 Hadwin D.

1 2015

Wyniki wyszukiwania

Unitarily invariant norms related to semi-finite factors