In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are homogeneous with respect to the action of the Möbius group consisting of bi-holomorphic automorphisms of the unit disc D. For every m ∈ N we have a family of operators depending on m+1 positive real parameters. The kernel function is calculated explicitly. It is proved that each o...

A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Calderón-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.

Certainly the best understood commutative Banach algebras are those that consist of all the continuous complex-valued functions on a compact Hausdorff space. Indeed, most self-adjoint phenomena involving them have been thoroughly investigated. In particular, the study of their representation theory as operators on a Hilbert space, which is essentially the spectral theory for normal operators, s...

ABSTRACT. Let Altn be the vector space of all alternating n × n complex matrices, on which the complex general linear group GLn acts by x 7→ gx tg. The aim of this paper is to show that Pfaffian of a certain matrix whose entries are multiplication operators or derivations acting on polynomials on Altn provides a generating function for the GLninvariant differential operators which play essentia...

For a quasi-free module over a function algebra A(Ω), we define an analogue of the Berezin transform and relate this to the quotient of the C*-algebra it generates modulo the commutator ideal. Certainly the best understood commutative Banach algebras are those that consist of all the continuous complex-valued functions on a compact Hausdorff space. Indeed, most self-adjoint phenomena involving ...