# Journal of Operator Theory

Volume 87, Issue 1, Winter 2022  pp. 187-201.

Maximum modulus principle for multipliers and mean ergodic multiplication operators

Authors:  Eugene Bilokopytov
Author institution:Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1 Canada

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2020aug11.2299
Keywords: function spaces, multiplication operators, mean ergodic operators