**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.**