For 1< p<∞ let Tpα be the norm closure of the algebra generated by Toeplitz operators with
bounded symbols acting on the standard weighted Fock space Fαp. In this paper, we will …

We study the so-called radial operators, and in particular radial Toeplitz operators, acting on
the standard weighted Bergman space on the unit ball in C^ n C n. They turn out to be …

In this paper, we study the compactness of operators on the Bergman space of the unit ball
and on very generally weighted Bargmann-Fock spaces in terms of the behavior of their …

We generalize several results on Toeplitz operators over reflexive, standard weighted Fock
spaces F pt to the non-reflexive cases p D 1; 1. Among these results are the characterization …

Abstract The Fredholm property of Toeplitz operators on the p-Fock spaces F_ α^ p F α p on
C^ n C n is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz …

We discuss the compactness of Hankel operators on Hardy, Bergman and Fock spaces with
focus on the differences between the three cases, and complete the theory of compact …

This paper discusses the convexity of the range of the Berezin transform. For a bounded
operator T acting on a reproducing kernel Hilbert space H (on a set X), this is the set B …

In this paper, we introduce techniques from complex harmonic analysis to prove a weaker
version of the Geometric Arveson-Douglas Conjecture on the Bergman space for a complex …

In this paper we consider the reproducing kernel thesis for boundedness and compactness
for various operators on Bergman-type spaces. In particular, the results in this paper apply to …

Extending recent results in [3] to the higher dimensional setting n⩾ 3 we provide a further
step in the structural analysis of a class of commutative Banach algebras generated by …