\(J\)-class operators and hypercyclicity. (English) Zbl 1243.47021
In this paper, the authors define the \(J\)-sets and examine some basic properties of these sets and investigate the relation between hypercyclicity and \(J\)-sets. They also introduce the notion of \(J\)-class operator and establish some of its properties and present examples of \(J\)-class operators which are not hypercyclic. At the end of the paper, they give a list of open problems.
Reviewer: Ömer Gök (Istanbul)