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  • Každý mocninově ohraničený operátor v reflexivním Banachově prostoru, jehož spektrum obsahuje 1, má netriviální invariantní kužel. (cs)
  • We show that each power bounded operator with spectral radius equal to one a reflexive Banach space 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 cone if 1 belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators. For non-reflexive Banach spaces these results remain true; however, the non-supercyclic vector (inavariant cone, respectively) relates to the adjoint of the operator.
  • We show that each power bounded operator with spectral radius equal to one a reflexive Banach space 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 cone if 1 belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators. For non-reflexive Banach spaces these results remain true; however, the non-supercyclic vector (inavariant cone, respectively) relates to the adjoint of the operator. (en)
Title
  • Power bounded operators and supercyclic vectors II
  • Mocninově ohraničené operátory a supercyklické vektory II (cs)
  • Power bounded operators and supercyclic vectors II (en)
skos:prefLabel
  • Power bounded operators and supercyclic vectors II
  • Mocninově ohraničené operátory a supercyklické vektory II (cs)
  • Power bounded operators and supercyclic vectors II (en)
skos:notation
  • RIV/67985840:_____/05:00030787!RIV06-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 2997;3004
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/03/0041), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 10
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 537403
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/05:00030787
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • supercyclic vectors; invariant subspace problem; positive operators (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [B7E385EBFFDD]
http://linked.open...i/riv/nazevZdroje
  • Proceedings of the American Mathematical Society
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 133
http://linked.open...iv/tvurceVysledku
  • Müller, Vladimír
http://linked.open...n/vavai/riv/zamer
issn
  • 0002-9939
number of pages
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