Power bounded operators and supercyclic vectors II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F05%3A00030787" target="_blank" >RIV/67985840:_____/05:00030787 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Power bounded operators and supercyclic vectors II
Original language description
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 hasa 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.
Czech name
Mocninově ohraničené operátory a supercyklické vektory II
Czech description
Každý mocninově ohraničený operátor v reflexivním Banachově prostoru, jehož spektrum obsahuje 1, má netriviální invariantní kužel.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F03%2F0041" target="_blank" >GA201/03/0041: Methods and function theory of Banach algebras in operator theory II.</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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