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1997 | 66 | 1 | 49-61
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Stable invariant subspaces for operators on Hilbert space

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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
  • Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300, U.S.A.
  • Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824, U.S.A.
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