Maximum Modulus Principle For Multipliers and Mean Ergodic Multiplication Operators
Functional Analysis
2020-08-11 v2
Abstract
The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are constants. As an application, a contractive multiplication operator is either a multiplication with a constant, or is completely non-unitary. Additionally we explore possibilities for a multiplication operator to be (weakly) compact and (uniformly) mean ergodic.
Cite
@article{arxiv.2007.11685,
title = {Maximum Modulus Principle For Multipliers and Mean Ergodic Multiplication Operators},
author = {Eugene Bilokopytov},
journal= {arXiv preprint arXiv:2007.11685},
year = {2020}
}
Comments
13 pages