Invertible and isometric weighted composition operators
Functional Analysis
2022-08-23 v2 Complex Variables
Abstract
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces. For the spaces of analytic functions in the disk whose norm is given in terms of a natural seminorm (such as the typical spaces given in terms of derivatives), we describe all surjective weighted composition operators that are isometric. This generalizes a number of known results.
Cite
@article{arxiv.2104.12220,
title = {Invertible and isometric weighted composition operators},
author = {Alejandro Mas and Dragan Vukotić},
journal= {arXiv preprint arXiv:2104.12220},
year = {2022}
}
Comments
In this version some references have been added and some misprints corrected