Positivity in the theory of supercyclic operators
Volume 75 / 2007
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.
