On hyponormality of Toeplitz operators. (English) Zbl 1525.47064

Sadraoui, Houcine; Garayev, Mubariz; Guediri, Hocine

Rocky Mt. J. Math. 51, No. 5, 1821-1831 (2021).

Summary: In this work we give sufficient conditions for hyponormality of Toeplitz operators on weighted Bergman spaces when the analytic part of the symbol is a monomial and the conjugate part is a polynomial. We also adapt a function theoretic method, due to P. Ahern and Ž. Čučković [Pac. J. Math. 173, No. 2, 295–305 (1996; Zbl 0962.47015)], to a class of Toeplitz operators on weighted Bergman spaces to get an extension of the necessary condition for hyponormality.

MSC:

47B35	Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B20	Subnormal operators, hyponormal operators, etc.
30H20	Bergman spaces and Fock spaces

Keywords:

Toeplitz operator; hyponormal operator; weighted Bergman space; polynomial symbol

Citations:

Zbl 0962.47015

References:

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