. . "0002-9939" . "3807;3812" . "Oper\u00E1tory s ohrani\u010Den\u00FDmi mocninami a supercyklick\u00E9 vektory"@cs . . "622169" . "1"^^ . . . "131" . . "Power bounded operators and supercyclic vectors" . "[F5716B5E43A6]" . "Podle zn\u00E1m\u00E9 v\u011Bty ( Brown-Chevreau-Pearcy ) ka\u017Ed\u00E1 kontrakce na Hilbertov\u011B prostoru, jej\u00ED\u017E spektrum obsahuje jednotkovou kru\u017Enici, m\u00E1 netrivi\u00E1ln\u00ED invariantn\u00ED podprostor. Tj. existuje nenulov\u00FD necyklick\u00FD vektor. Zde je uk\u00E1z\u00E1no, \u017Ee ka\u017Ed\u00FD oper\u00E1tor s ohrani\u010Den\u00FDmi mocninami, jeho\u017E spektr\u00E1ln\u00ED polom\u011Br je roven 1, m\u00E1 nenulov\u00FD vektor, kter\u00FD nen\u00ED supercyklick\u00FD."@cs . . "P(GA201/03/0041), Z(AV0Z1019905)" . . . "RIV/67985840:_____/03:00106806!RIV/2005/GA0/A05005/N" . "1"^^ . "Power bounded operators and supercyclic vectors"@en . . . . . . . "RIV/67985840:_____/03:00106806" . "supercyclic vector;invariant subspace problem;power bounded operator"@en . "6"^^ . "Oper\u00E1tory s ohrani\u010Den\u00FDmi mocninami a supercyklick\u00E9 vektory"@cs . "12" . "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." . . . "Power bounded operators and supercyclic vectors" . "M\u00FCller, Vladim\u00EDr" . "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."@en . "Power bounded operators and supercyclic vectors"@en . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "Proceedings of the American Mathematical Society" .