51. Complex symmetric monomial Toeplitz operators on the unit ball
- Author
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Xing-Tang Dong, Ze-Hua Zhou, and Xiao-He Hu
- Subjects
Unit sphere ,Mathematics::Functional Analysis ,Matrix (mathematics) ,Pure mathematics ,Monomial ,Bergman space ,Applied Mathematics ,Extension (predicate logic) ,Commutative algebra ,Analysis ,Toeplitz matrix ,Mathematics ,Toeplitz operator - Abstract
Monomial Toeplitz operators T z p z ¯ q on the weighted Bergman space of the unit ball in C n are natural extension of the weighted shift operators. In higher dimensions, dim ker T z p z ¯ q = ∞ may occur for non-trivial case, thus complex symmetric phenomena will appear. In this paper, we completely characterize when the monomial Toeplitz operator T z p z ¯ q on the weighted Bergman space is J A -symmetric, where J A f ( z ) = f ( A z ‾ ) ‾ with the symmetric unitary n × n matrix A. Moreover, we also determine all possible forms of A such that T z p z ¯ q is J A -symmetric. As an application, we construct the weakly closed unital commutative algebra generated by complex symmetric Toeplitz operators.
- Published
- 2020