Abstract
In this paper, we give an alternative characterization of complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we prove that a block Toeplitz operator (Formula presented.) is complex symmetric with the conjugation (Formula presented.) on the vector-valued Hardy space (Formula presented.) if and only if (Formula presented.), where (Formula presented.) denotes the multiplication operator on (Formula presented.) with symbol Φ. As some applications, we provide examples of normal (resp., non-normal) complex symmetric block Toeplitz operators.
| Original language | English |
|---|---|
| Pages (from-to) | 3466-3476 |
| Number of pages | 11 |
| Journal | Linear and Multilinear Algebra |
| Volume | 70 |
| Issue number | 18 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Funding Information:The first-named author was supported by the National Research Foundation of Korea [NRF-2019R1H1A1102084]. The second-named author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) [2019R1F1A1058633] and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177). The third-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [2019R1A2C1002653]. The authors would like to thank the referee for his/her valuable comments which hepled to improve the paper.
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Keywords
- Block Toeplitz operator
- Complex symmetric operator
- Toeplitz operator
- conjugation