The essential norm of a composition operator on the minimal Mobius invariant space
Complex Variables
2010-08-05 v2
Abstract
We derive a formula for the essential norm of a composition operator on the minimal Mobius invariant space of analytic functions. As an application, we show that the essential norm of a non-compact composition operator is at least 1. We also obtain lower bounds depending on the behavior of the symbol near the boundary, and calculate the order of magnitude of the essential norm of composition operators induced by finite Blaschke products.
Keywords
Cite
@article{arxiv.1005.4935,
title = {The essential norm of a composition operator on the minimal Mobius invariant space},
author = {Themis Mitsis and Michael Papadimitrakis},
journal= {arXiv preprint arXiv:1005.4935},
year = {2010}
}
Comments
11 pages