Symmetric analytic functions on the Cartesian power of the complex Banach space of Lebesgue measurable essentially bounded functions on [0,1

Abstract

This work is devoted to the study of the Fréchet algebra Hbs((L∞[0,1])n) of all symmetric (invariant under composition of the variable with any measure preserving bijection of [0,1]) complex-valued analytic entire functions, which are bounded on bounded sets, on the nth Cartesian power (L∞[0,1])n of the complex Banach space L∞[0,1] of Lebesgue measurable essentially bounded complex-valued functions on [0,1]. We describe the spectrum (the set of all nontrivial continuous linear multiplicative functionals (characters)) of the Fréchet algebra Hbs((L∞[0,1])n). We show that every character of this Fréchet algebra is a point-evaluation functional.