| Title:
|
Recurrence and mixing recurrence of multiplication operators (English) |
| Author:
|
Amouch, Mohamed |
| Author:
|
Lakrimi, Hamza |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
1-11 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a Banach space, $\mathcal {B}(X)$ the algebra of bounded linear operators on $X$ and $(J, \|{\cdot }\|_{J})$ an admissible Banach ideal of $\mathcal {B}(X)$. For $T\in \mathcal {B}(X)$, let $L_{J, T}$ and $R_{J, T}\in \mathcal {B}(J)$ denote the left and right multiplication defined by $L_{J, T}(A)=TA$ and $R_{J, T}(A)=AT$, respectively. In this paper, we study the transmission of some concepts related to recurrent operators between $T\in \mathcal {B}(X)$, and their elementary operators $L_{J, T}$ and $R_{J, T}$. In particular, we give necessary and sufficient conditions for $L_{J, T}$ and $R_{J, T}$ to be sequentially recurrent. Furthermore, we prove that $L_{J, T}$ is recurrent if and only if $T\oplus T$ is recurrent on $X\oplus X$. Moreover, we introduce the notion of a mixing recurrent operator and we show that $L_{J, T}$ is mixing recurrent if and only if $T$ is mixing recurrent. (English) |
| Keyword:
|
hypercyclicity |
| Keyword:
|
recurrent operator |
| Keyword:
|
left multiplication operator |
| Keyword:
|
right multiplication operator |
| Keyword:
|
tensor product |
| Keyword:
|
Banach ideal of operators |
| MSC:
|
37B20 |
| MSC:
|
47A16 |
| MSC:
|
47B47 |
| DOI:
|
10.21136/MB.2023.0047-22 |
| . |
| Date available:
|
2024-03-13T10:15:25Z |
| Last updated:
|
2024-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152286 |
| . |
| Reference:
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