Stable invariant subspaces for operators on Hilbert space

• Autorzy: John B. Conway , Don Hadwin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

invariant subspace; stability; normal operators

Kategorie tematyczne

• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 49-61

Daty

wydano

1997

otrzymano

1995-10-23

Twórcy

autor

John B. Conway

• Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300, U.S.A.

autor

Don Hadwin

• Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824, U.S.A.

Bibliografia

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