Hypercyclicity on the algebra of Hilbert–Schmidt operators. (English) Zbl 1080.47013

Authors’ abstract: We prove that the hypercyclicity criterion for any operator \(T\) on a Hilbert space is equivalent to the hypercyclicity of the left multiplication operator induced by \(T\) on the algebra of Hilbert–Schmidt operators.


47A16 Cyclic vectors, hypercyclic and chaotic operators
47L10 Algebras of operators on Banach spaces and other topological linear spaces
Full Text: DOI


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