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Supercyclicity in the operator algebra using Hilbert-Schmidt operators. (English) Zbl 1196.47009
Summary: We prove that the supercylicity criterion for any operator \(T\) on a Hilbert space is equivalent to the supercyclicity of the left multiplication operator induced by \(T\) in the strong operator topology.

47A16 Cyclic vectors, hypercyclic and chaotic operators
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Full Text: DOI
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