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SEMINARIO DE ANÁLISIS COMPLEJO
(COMPLEX ANALYSIS SEMINAR)
Weighted composition operators: an axiomatic approach
DRAGAN VUKOTI´C,
UAM
Jueves, 3 de mayo de 2018 a las 14:30
(Thursday,May 3, 2018 at 14:30)
Aula/Room 520, Módulo/Module 17
Departamento deMatemáticas, UAM
Resumen / Abstract:
Weighted composition operators (WCO) are defined as a composition follo-
wed by multiplication. They are very natural and frequently studied objects in
Complex Analysis and Operator Theory and are related to several fundamen-
tal questions in these areas.
In this joint work with Irina Arévalo, we considerWCOs acting on very general
Banach spaces of analytic functions in the disk or other domains that satisfy
only a minimum number of natural axioms.
Among the preliminary results, we discuss some implications of the basic
axioms and identify all functional Banach spaces in which every bounded
analytic function is a pointwise multiplier. Next, we characterize (in various
ways) the weighted composition operators among the bounded operators on
such spaces, thus generalizing some well-known results on multiplication or
composition operators.
As a main result, we also characterize the invertible weighted composition
operators on the disk and on general Banach spaces of analytic functions on
bounded domains under different sets of axioms whose connections we dis-
cuss by providing appropriate examples. This generalizes and complements
various recent results by Gunatillake, Bourdon, and Hyvärinen-Lindström-
Nieminen-Saukko.