On the Salas Theorem and Hypercyclicity of f(T)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00373153" target="_blank" >RIV/67985840:_____/10:00373153 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00020-010-1791-x" target="_blank" >http://dx.doi.org/10.1007/s00020-010-1791-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00020-010-1791-x" target="_blank" >10.1007/s00020-010-1791-x</a>

Result language
angličtina
Original language name
On the Salas Theorem and Hypercyclicity of f(T)
Original language description
We study hypercyclicity properties of functions of Banach space operators. Generalizations of the results of Herzog-Schmoeger and Bermudez-Miller are obtained. As a corollary we also show that each non-trivial operator commuting with a generalized backward shift is supercyclic. This gives a positive answer to a conjecture of Godefroy and Shapiro. Furthermore, we show that the norm-closures of the set of all hypercyclic (mixing, chaotic, frequently hypercyclic, respectively) operators on a Hilbert spacecoincide. This implies that the set of all hypercyclic operators that do not satisfy the hypercyclicity criterion is rather small-of first category (in the norm-closure of hypercyclic operators).
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F09%2F0473" target="_blank" >GA201/09/0473: Methods of function theory and Banach algebras in operator theory IV</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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