(untitled) (Baghdad Science Journal, 2024)
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