On chaoticity of the sum of chaotic shifts with their adjoints in Hilbert space and applications to some chaotic weighted shifts acting on some Fock-Bargmann spaces

TL;DR

This paper investigates the chaotic behavior of certain unbounded backward shift operators and their sums with adjoints on Fock-Bargmann spaces, providing conditions under which these operators exhibit chaos.

Contribution

It introduces sufficient conditions for the sum of a chaotic shift operator and its adjoint to be chaotic on Hilbert spaces.

Findings

Chaoticity of specific backward shift operators on Fock-Bargmann spaces.

Conditions for the sum of a chaotic shift and its adjoint to be chaotic.

Analysis of unbounded differential operators in the context of chaos.

Abstract

This article is intended to outline some the recent work by the author on the chaoticity of some specific bakward shift unbounded operators realized as differential operators acting on some Fock-Bargmann spaces and give suficient conditions on a linear unbounded densely defined chaotic shift operator $T$ acting on a Hilbert space for the operator $T+T^*$ to be chaotic where $T^*$ is its adjoint.