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Stable invariant subspaces for operators on Hilbert space

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Conway J., Hadwin D.

Annales Polonici Mathematici

1997

tom 66

nr 1

49-61

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 ${ℳ_n}$, with $ℳ_n$ in $Lat T_n$ for all n, such that $P_{ℳ_n} → P_{ℳ}$ 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 in these cases the stable invariant subspaces are the strong closure of the norm stable invariant subspaces.

Unitarily invariant norms related to semi-finite factors

100%

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 Annales Polonici Mathematici

1 Studia Mathematica

2 Hadwin D.

1 Conway J.

1 Fang J.

1 2015

1 1997

Wyniki wyszukiwania

Stable invariant subspaces for operators on Hilbert space

Unitarily invariant norms related to semi-finite factors