Limits of J-class operators

TL;DR

This paper provides a spectral description of the closure of J-class operators on separable Hilbert spaces, addressing an open problem in the field of operator theory.

Contribution

It offers the first spectral characterization of the closure of J-class operators, solving an open problem posed by Costakis and Manoussos.

Findings

Spectral description of the closure of J-class operators

Resolution of an open problem in operator theory

Advancement in understanding hypercyclicity and J-class operators

Abstract

The purpose of the present work is to answer an open problem which is raised by G.Costakis and A.Manoussos in their paper "J-class operators and hypercyclicity " accepted by J. Operator Theory. More precisely, we give the spectral description of the closure of the set of J-class operators acting on a separable Hilbert space.