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

This work is devoted to the study of the Frechet algebra H-bs ((L infinity[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 infinity[0,1])(n) of the complex Banach space L infinity[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 Frechet algebra H-bs ((L infinity[0, 1])(n)). We show that every character of this Frechet algebra is a point-evaluation functional.(c) 2022 Elsevier Inc. All rights reserved.