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  • Podle známé věty ( Brown-Chevreau-Pearcy ) každá kontrakce na Hilbertově prostoru, jejíž spektrum obsahuje jednotkovou kružnici, má netriviální invariantní podprostor. Tj. existuje nenulový necyklický vektor. Zde je ukázáno, že každý operátor s ohraničenými mocninami, jehož spektrální poloměr je roven 1, má nenulový vektor, který není supercyklický. (cs)
  • 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.
  • 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)
Title
  • Power bounded operators and supercyclic vectors
  • Power bounded operators and supercyclic vectors (en)
  • Operátory s ohraničenými mocninami a supercyklické vektory (cs)
skos:prefLabel
  • Power bounded operators and supercyclic vectors
  • Power bounded operators and supercyclic vectors (en)
  • Operátory s ohraničenými mocninami a supercyklické vektory (cs)
skos:notation
  • RIV/67985840:_____/03:00106806!RIV/2005/GA0/A05005/N
http://linked.open.../vavai/riv/strany
  • 3807;3812
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/03/0041), Z(AV0Z1019905)
http://linked.open...iv/cisloPeriodika
  • 12
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  • 622169
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  • RIV/67985840:_____/03:00106806
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  • supercyclic vector;invariant subspace problem;power bounded operator (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [F5716B5E43A6]
http://linked.open...i/riv/nazevZdroje
  • Proceedings of the American Mathematical Society
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  • 131
http://linked.open...iv/tvurceVysledku
  • Müller, Vladimír
http://linked.open...n/vavai/riv/zamer
issn
  • 0002-9939
number of pages
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