Recurrency on the Space of Hilbert-Schmidt Operators
DOI:
https://doi.org/10.21123/bsj.2023.8870Keywords:
Hilbert-Schmidt Operators, Hypercyclic Operators, Left Multiplication, Recurrent Operators, Recurrent SemigroupAbstract
In this paper, it is proved that if a C0-semigroup is chaotic, hypermixing or supermixing, then the related left multiplication C0-semigroup on the space of Hilbert-Schmidt operators is recurrent if and only if it is hypercyclic. Also, it is stated that under some conditions recurrence of a C0-semigroup and the recurrency of the left multiplication C0-semigroup that is related to it, on the space of Hilbert-Schmidt operators are equivalent. Moreover, some sufficient conditions for recurrency and hypercyclicity of the left multiplication C0-semigroup are presented that are based on dense subsets
Received 07/04/2023
Revised 15/07/2023
Accepted 17/07/2023
Published Online First 20/10/2023
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