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

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