Abstract
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
Keywords
Hilbert-Schmidt Operators, Hypercyclic Operators, Left Multiplication, Recurrent Operators, Recurrent Semigroup
Article Type
Article
How to Cite this Article
Moosapoor, Mansooreh
(2024)
"Recurrency on the Space of Hilbert-Schmidt Operators,"
Baghdad Science Journal: Vol. 21:
Iss.
5, Article 22.
DOI: https://doi.org/10.21123/bsj.2023.8870
