Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces
Volume 170 / 2005
Studia Mathematica 170 (2005), 57-75
MSC: Primary 47A16; Secondary 47D03.
DOI: 10.4064/sm170-1-3
Abstract
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.
