Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces

Tom 170 / 2005

Teresa Bermúdez, Antonio Bonilla, José A. Conejero, Alfredo Peris Studia Mathematica 170 (2005), 57-75 MSC: Primary 47A16; Secondary 47D03. DOI: 10.4064/sm170-1-3

Streszczenie

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.

Autorzy

  • Teresa BermúdezDepartamento de Análisis Matemático
    Universidad de La Laguna
    E-38271 La Laguna (Tenerife), Spain
    e-mail
  • Antonio BonillaDepartamento de Análisis Matemático
    Universidad de La Laguna
    E-38271 La Laguna (Tenerife), Spain
    e-mail
  • José A. ConejeroFacultat d'Informàtica
    Departament de Matemàtica Aplicada
    and IMPA
    Universitat Politècnica de València
    E-46022 València, Spain
    e-mail
  • Alfredo PerisE.T.S. Arquitectura
    Departament de Matemàtica Aplicada
    and IMPA
    Universitat Politècnica de València
    E-46022 València, Spain
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek