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  • 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 space coincide. 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).
  • 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 space coincide. 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). (en)
Title
  • On the Salas Theorem and Hypercyclicity of f(T)
  • On the Salas Theorem and Hypercyclicity of f(T) (en)
skos:prefLabel
  • On the Salas Theorem and Hypercyclicity of f(T)
  • On the Salas Theorem and Hypercyclicity of f(T) (en)
skos:notation
  • RIV/67985840:_____/10:00373153!RIV12-AV0-67985840
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  • P(GA201/09/0473), Z(AV0Z10190503)
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  • 3
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  • 276919
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  • RIV/67985840:_____/10:00373153
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  • supercyclic operators; hypercyclicity criterion; Salas' theorem (en)
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  • CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV
  • [FD8EEAE6C89E]
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  • Integral Equations and Operator Theory
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  • 67
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  • Müller, Vladimír
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  • 000279210600007
http://linked.open...n/vavai/riv/zamer
issn
  • 0378-620X
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s00020-010-1791-x
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