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Complex symmetric Toeplitz operators on the unit polydisk.
- Source :
-
International Journal of Mathematics . Jan2023, Vol. 34 Issue 1, p1-25. 25p. - Publication Year :
- 2023
-
Abstract
- In this paper, we study the complex symmetry of Toeplitz operators on the weighted Bergman spaces over the unit polydisk. First, we completely characterize when anti-linear weighted composition operators W ψ , φ J are conjugations. We then give a sufficient and necessary condition for Toeplitz operators to be complex symmetric with respect to these conjugations. As a consequence, some interesting higher-dimensional complex symmetric phenomena appear on the unit polydisk such as the monomial Toeplitz operators T z p z ¯ q with p = V q for some symmetric permutation matrix V. Surprisingly, these operators T z V q z ¯ q are the only ones that are complex symmetric monomial Toeplitz operators on the unit bidisk. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 34
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 162060573
- Full Text :
- https://doi.org/10.1142/S0129167X22500963