There has been a flurry of activity in recent years in the loosely defined area of holomorphic
spaces. This book discusses the most well-known and widely used spaces of holomorphic …

Preliminary Text. Do not use. 15 years ago the function theory and operator theory
connected with the Hardy spaces was well understood (zeros; factorization; interpolation; …

This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric
functional analysis which deals with certain subspaces of Banach spaces arising naturally in …

The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on
the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S …

This unique book is devoted to the detailed study of the recently discovered commutative C*-
algebras of Toeplitz operators on the Bergman space over the unit disk. Surprisingly, the key …

A characterization of compact difference is given for composition operators acting on the
standard weighted Bergman spaces and necessary conditions are given on a larger scale of …

This revised and extended edition of a well-established monograph in function theory
contains a study on various function classes on the disc, a number of new results and new or …

Shift operators on Hilbert spaces of analytic functions play an important role in the study of
bounded linear operators on Hilbert spaces since they often serve as “models” for various …

Let D be the open unit disk in C and dA the normalized area measure on D. For 1< p<+ co,
the analytic Besov space BP consists of analytic functionsfon D such that (1-Izl') f'(z) is in LP …