On the Salas Theorem and Hypercyclicity of f(T)

0373153 - MÚ 2012 RIV CH eng J - Článek v odborném periodiku
Müller, Vladimír
On the Salas Theorem and Hypercyclicity of f(T).
Integral Equations and Operator Theory. Roč. 67, č. 3 (2010), s. 439-448. ISSN 0378-620X. E-ISSN 1420-8989
Grant CEP: GA ČR GA201/09/0473
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: supercyclic operators * hypercyclicity criterion * Salas' theorem
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.521, rok: 2010
http://www.springerlink.com/content/f245731531550638/

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).
Trvalý link: http://hdl.handle.net/11104/0206307