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Article Dans Une Revue Journal of Operator Theory Année : 2013

Stable and Norm-stable Invariant Subspaces

Résumé

We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are the finite-dimensional ones. We also characterize norm-stable invariant subspaces of any weighted unilateral shift operator. We show that quasianalytic shift operators are points of norm continuity of the lattice of the invariant subspaces. We also provide a necessary condition for strongly stable invariant subspaces for certain operators.

Dates et versions

hal-01257824 , version 1 (18-01-2016)

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Alexander Borichev, Don Hadwin, Hassan Yousefi. Stable and Norm-stable Invariant Subspaces. Journal of Operator Theory, 2013, 69 (1), pp.3-16. ⟨10.7900/jot.2010jun01.1866⟩. ⟨hal-01257824⟩
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