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• W2036009654 abstract "By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant positive cone." @default.
• W2036009654 created "2016-06-24" @default.
• W2036009654 creator A5083530338 @default.
• W2036009654 date "2003-03-25" @default.
• W2036009654 modified "2023-09-24" @default.
• W2036009654 title "Power bounded operators and supercyclic vectors" @default.
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• W2036009654 doi "https://doi.org/10.1090/s0002-9939-03-06962-4" @default.
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