Norm attaining composition operators on Segal-Bargmann spaces

Abstract

In this note, we study the composition operators on Segal-Bargmann spaces, which attains its norm and we show that every composition operators on the classical Fock space over ${\mathbb{C}}^n$ is norm attaining. Also, we establish a necessary and sufficient condition for a sum of two kernel functions to be an extremal function for the norm of composition operators.

12 Pages