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Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces

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Bermúdez T., Bonilla A., Conejero J., Peris A.

Studia Mathematica

2005

tom 170

nr 1

57-75

Our aim in this paper is to prove that every separable infinite-dimensional complex Banach space admits a topologically mixing holomorphic uniformly continuous semigroup and to characterize the mixing property for semigroups of operators. A concrete characterization of being topologically mixing for the translation semigroup on weighted spaces of functions is also given. Moreover, we prove that there exists a commutative algebra of operators containing both a chaotic operator and an operator which is not a multiple of the identity and no multiple of which is chaotic. This gives a negative answer to a question of deLaubenfels and Emamirad.

Ograniczanie wyników

1 Studia Mathematica

1 Bermúdez T.

1 Bonilla A.

1 Conejero J.

1 Peris A.

1 2005

Wyniki wyszukiwania

Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces