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On λ-commuting operators

100%

Conway J., Prǎjiturǎ G.

Studia Mathematica

2005

tom 166

nr 1

1-9

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.

Stable invariant subspaces for operators on Hilbert space

100%

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

2 Conway J.

1 Hadwin D.

1 Prǎjiturǎ G.

1 2005

1 1997

Wyniki wyszukiwania

On λ-commuting operators

Stable invariant subspaces for operators on Hilbert space