Disjoint mixing operators

Juan Bes, Ozgur Martin, Alfred Peris, Stanislav Shkarin

Research output: Contribution to journalArticle

49 Citations (Scopus)
37 Downloads (Pure)

Abstract

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.
Original languageEnglish
Pages (from-to)1283-1322
Number of pages40
JournalJournal of Functional Analysis
Volume263
Issue number5
DOIs
Publication statusPublished - 01 Sep 2012

ASJC Scopus subject areas

  • Analysis

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