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Hypercyclic Operators on Hilbert C*-modules (2301.12265v2)
Published 28 Jan 2023 in math.OA and math.FA
Abstract: In this paper, we characterize hypercyclic generalized bilateral weighted shift operators on the standard Hilbert module over the C*-algebra of compact operators on the separable Hilbert space. Moreover, we give necessary and sufficient conditions for these operators to be chaotic and we provide concrete examples. In addition, we characterize a class of hypercyclic operators on non-unital C*-algebras and we provide concrete examples.