Positivity in the theory of supercyclic operators

  1. León-Saavedra, F. 1
  2. Piqueras-Lerena, A. 2
  1. 1 Universidad de Cádiz
    info

    Universidad de Cádiz

    Cádiz, España

    ROR https://ror.org/04mxxkb11

  2. 2 Department of Mathematics, University of Cádiz. Escuela Superior de Ingeniería. C/ Sacramento, 82, 11002 Cádiz, Spain
Konferenzberichte:
Stefan Banach International Mathematical Center

Verlag: INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES

ISSN: 0137-6934

Datum der Publikation: 2007

Art: Konferenz-Beitrag

DOI: 10.4064/BC75-0-13 GOOGLE SCHOLAR

Zusammenfassung

A bounded linear operator T defined on a Banach space X is said to be supercyclic if there exists a vector x ∈ X such that the projective orbit {λT nx : λ ∈ C, n ∈ N} is dense in X. The aim of this survey is to show the relationship between positivity and supercyclicity. This relationship comes from the so called Positive Supercyclicity Theorem. Throughout this exposition, interesting new directions and open problems will appear.