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

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.