A note on composition operators in a half-plane
Functional Analysis
2012-05-08 v1
Abstract
Conditions for a composition operator on the Hardy space of the disk to have closed range or be similar to an isometry are well known. We provide such conditions for composition operators on the Hardy space of the upper half-plane. We also show that the operator of composition with an analytic self-map \Phi\ of the upper half-plane can be similar to an isometry even when \Phi\ is far from being an inner function.
Cite
@article{arxiv.1205.1489,
title = {A note on composition operators in a half-plane},
author = {Hari Bercovici and Dan Timotin},
journal= {arXiv preprint arXiv:1205.1489},
year = {2012}
}