Positivity in the theory of supercyclic operators

Volume 75 / 2007

F. León-Saavedra, A. Piqueras-Lerena Banach Center Publications 75 (2007), 221-232 MSC: Primary 47B37; Secondary 47B38, 47B99. DOI: 10.4064/bc75-0-13

Abstract

A bounded linear operator $T$ defined on a Banach space $X$ is said to be supercyclic if there exists a vector $x\in X$ such that the projective orbit $\{\lambda T^nx\,\, :\, \lambda \in \mathbb C, \, n\in\mathbb N\}$ 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.

Authors

  • F. León-SaavedraDepartment of Mathematics
    University of Cádiz
    Campus Universitario de Jerez de la Frontera
    Avda. de la Universidad s//n
    11402 Jerez de la Frontera (Cádiz)
    Spain
    e-mail
  • A. Piqueras-LerenaDepartment of Mathematics
    University of Cádiz
    Escuela Superior de Ingeniería
    C/ Sacramento, 82
    11002 Cádiz
    Spain
    e-mail

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