Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces

• Autorzy: Teresa Bermúdez , Antonio Bonilla , José A. Conejero , Alfredo Peris
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 47D03: Groups and semigroups of linear operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 1
• Strony: 57-75

Daty

wydano

2005

Twórcy

autor

Teresa Bermúdez

• Departamento de Análisis Matemático, Universidad de La Laguna, E-38271 La Laguna (Tenerife), Spain

autor

Antonio Bonilla

• Departamento de Análisis Matemático, Universidad de La Laguna, E-38271 La Laguna (Tenerife), Spain

autor

José A. Conejero

• Facultat d'Informàtica, Departament de Matemàtica Aplicada, and IMPA, Universitat Politècnica de València, E-46022 València, Spain

autor

Alfredo Peris

• E.T.S. Arquitectura, Departament de Matemàtica Aplicada, and IMPA, Universitat Politècnica de València, E-46022 València, Spain

Identyfikatory

DOI

10.4064/sm170-1-3