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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.

##### MSC:
 47A16 Cyclic vectors, hypercyclic and chaotic operators 47L10 Algebras of operators on Banach spaces and other topological linear spaces
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##### References:
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