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Unitarily invariant norms related to semi-finite factors

Junsheng FangDon Hadwin — 2015

Studia Mathematica

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,...

Stable invariant subspaces for operators on Hilbert space

John B. ConwayDon Hadwin — 1997

Annales Polonici Mathematici

If T is a bounded operator on a separable complex Hilbert space ℋ, an invariant subspace ℳ for T is stable provided that whenever T n is a sequence of operators such that T n - T 0 , there is a sequence of subspaces n , with n in L a t T n for all n, such that P n P in the strong operator topology. If the projections converge in norm, ℳ is called a norm stable invariant subspace. This paper characterizes the stable invariant subspaces of the unilateral shift of finite multiplicity and normal operators. It also shows that...

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