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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...

On λ-commuting operators

John B. ConwayGabriel Prǎjiturǎ — 2005

Studia Mathematica

For a scalar λ, two operators T and S are said to λ-commute if TS = λST. In this note we explore the pervasiveness of the operators that λ-commute with a compact operator by characterizing the closure and the interior of the set of operators with this property.

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