Let A be a complex unital Banach algebra and M be a left A-module. Let Ʌ: M→ℂ be a map that is not necessarily linear. We establish conditions for Ʌ to be linear and of multiplicative kind, from its behavior on a small subset of M. We do not assume Ʌ to be continuous throughout. As an application, we give a characterization of weighted composition operators on the Hardy space H. © Instytut Matematyczny PAN. 2021.

Sukumar Daniel

Department of Mathematics

G. Sebastian

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Journal	Colloquium Mathematicum
Publisher	Institute of Mathematics. Polish Academy of Sciences
ISSN	00101354