Recurrency on the Space of Hilbert-Schmidt Operators
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-semi...
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University of Baghdad, College of Science for Women
2024-05-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8870 |
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| author | Mansooreh Moosapoor |
| author_facet | Mansooreh Moosapoor |
| author_sort | Mansooreh Moosapoor |
| collection | DOAJ |
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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
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| format | Article |
| id | doaj-art-051b6a1729d040fb85cc725efbe52b95 |
| institution | DOAJ |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-051b6a1729d040fb85cc725efbe52b952025-08-20T03:15:51ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862024-05-0121510.21123/bsj.2023.8870Recurrency on the Space of Hilbert-Schmidt OperatorsMansooreh Moosapoor0https://orcid.org/0000-0003-4194-6495Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran. 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 https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8870Hilbert-Schmidt Operators, Hypercyclic Operators, Left Multiplication, Recurrent Operators, Recurrent Semigroup |
| spellingShingle | Mansooreh Moosapoor Recurrency on the Space of Hilbert-Schmidt Operators مجلة بغداد للعلوم Hilbert-Schmidt Operators, Hypercyclic Operators, Left Multiplication, Recurrent Operators, Recurrent Semigroup |
| title | Recurrency on the Space of Hilbert-Schmidt Operators |
| title_full | Recurrency on the Space of Hilbert-Schmidt Operators |
| title_fullStr | Recurrency on the Space of Hilbert-Schmidt Operators |
| title_full_unstemmed | Recurrency on the Space of Hilbert-Schmidt Operators |
| title_short | Recurrency on the Space of Hilbert-Schmidt Operators |
| title_sort | recurrency on the space of hilbert schmidt operators |
| topic | Hilbert-Schmidt Operators, Hypercyclic Operators, Left Multiplication, Recurrent Operators, Recurrent Semigroup |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8870 |
| work_keys_str_mv | AT mansoorehmoosapoor recurrencyonthespaceofhilbertschmidtoperators |