The Bergman space as a Banach algebra
In this paper we use the Duhamel product to provide a Banach algebra structure to each of a scale of Bergman spaces over the unit disk, and then carry out many interesting consequences. In particular we characterize cyclic vectors of the Volterra integration operator, and determine its extended eigenvalues and corresponding extended eigenoperators. We also identify its commutants and point out some intertwining relations between the Volterra integration operator and composition operators.
In this paper we use the Duhamel product to provide a Banach algebra structure to each of a scale of Bergman spaces over the unit disk, and then carry out many interesting consequences.
We characterize skew-symmetric operators on a reproducing kernel Hilbert space in terms of their
Berezin symbols. The solution of some operator equations with skew-symmetric operators is…