Hypercyclic and topologically mixing cosine functions on Banach spaces

Our first aim in this paper is to give sufficient conditions for the hypercyclicity and topological mixing of a strongly continuous cosine function. We apply these results to study the cosine function associated to translation groups. We also prove that every separable infinite dimensional complex B...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-02, Vol.136 (2), p.519-528
Main Authors: Bonilla, Antonio, Miana, Pedro J.
Format: Article
Language:English
Subjects:
Banach space
Cosine function
Exact sciences and technology
Frechet topologies
Functional analysis
General mathematics
General, history and biography
Global analysis, analysis on manifolds
Linear transformations
Mathematical analysis
Mathematics
Real functions
Sciences and techniques of general use
Semigroups
Topological spaces
Topological theorems
Topological vector spaces
Topology
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Our first aim in this paper is to give sufficient conditions for the hypercyclicity and topological mixing of a strongly continuous cosine function. We apply these results to study the cosine function associated to translation groups. We also prove that every separable infinite dimensional complex Banach space admits a topologically mixing uniformly continuous cosine family.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-07-09036-3