Toeplitz Operators and Composition Operators on the q-Bergman Space
In this work we consider Toeplitz operators and composition operators on the q-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition for hyponormality of Toeplitz operators in the case of a symbol where the analytic part is a monomial. We also give a necessary condition for hyponormality in the general case of a harmonic symbol as well as a necessary and sufficient condition for such operators to commute. For composition operators we give necessary conditions and sufficient conditions for their compactness and normality, as well as necessary conditions for cohyponormality in the case of a linear fractional map and we finally compute the adjoint in the case of a linear map.
We show that the q-Bergman space with the Duhamel product has a
Banach algebra structure and describe its nontrivial closed ideals. Moreover, we discuss
Katznelson–Tzafriri type…
A bounded operator S on a Hilbert space is hyponormal if S∗S−SS∗ is positive. In this work we find necessary conditions for the hyponormality of the Toeplitz operator Tφ+ψ¯ on the Bergman…
In this work we consider Toeplitz operators and composition operators on the q-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition…