Stable invariant subspaces for operators on Hilbert space

John B. Conway; Don Hadwin

Annales Polonici Mathematici, Tome 66 (1997), p. 49-61 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $‖ T_{n} - T ‖ \to 0$ , there is a sequence of subspaces $ℳ_{n}$ , with $ℳ_{n}$ in $L a t T_{n}$ for all n, such that $P_{ℳ_{n}} \to P_{ℳ}$ 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.

Publié le : 1997-01-01

Zbl 0874.47004

EUDML-ID : urn:eudml:doc:269992

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     title = {Stable invariant subspaces for operators on Hilbert space},
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     year = {1997},
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John B. Conway; Don Hadwin. Stable invariant subspaces for operators on Hilbert space. Annales Polonici Mathematici, Tome 66 (1997) pp. 49-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p49bwm/

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