Interpolationseigenschaften des Spektrums linearer Operatoren auf Lp-Räumen.
Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.
The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω. The main result reads as follows: Assume that B is a Banach space of analytic functions...
We investigate isometric composition operators on the weighted Dirichlet space with standard weights , . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space . We solve some of these but not in general. We also investigate the situation when is equipped with another equivalent norm.
Let be a measure on a domain in such that the Bergman space of holomorphic functions in possesses a reproducing kernel and . The Berezin transform associated to is the integral...