We study the invariant subspace structure of the operator of multiplication by $ z $, ${M_z} $,
on a class of Banach spaces of analytic functions. For operators on Hilbert spaces our class …

In this paper we study holomorphic families of subspaces of a Banach space, which are
parametrized by some analytic space. We consider the question of the existence of a …

Let D denote the open unit disc (ze C:| z|< 1), let T denote the boundary (ze C:| z|= 1), and let
DT denote the closure of D. By A= A (D) we denote the disc algebra, consisting of those …

Many interesting Hilbert space operators can be modelled by natural operations on spaces
of functions analytic in the unit disk D. The most basic of these operations is multiplication by …

We characterize the surjective isometries of a class of analytic functions on the disk which
include the Analytic Besov space B p and the Dirichlet space D p. In the case of B p we are …

On generalized Bergman spaces Page 1 On generalized Bergman spaces Wolfgang Lusky
Abstract 1 Let D be the open unit disc and µ a positive bounded measure on [0,1]. Extending …

In the past few years operator theorists have been studying the problem of solving systems
of simultaneous equations of a particular type in the predual of certain dual operator …

Let [] be the open unit disk in the complex plane [Copf]. The Bergman space L2a ([]) is the
Hilbert space of analytic functions f in [] such thatformula herewhere dA is the normalized …

A complete description is obtained for the subspaces of the Hardy space Hp (p⩾ 1) that are
invariant under the Volterra integral operator. We then show that this result can be applied to …

Let be the open unit ball in ℂ d, d≧ 1, and Hd 2 be the space of analytic functions on
determined by the reproducing kernel (1−< z, λ>)− 1. This reproducing kernel Hilbert space …