Spectra of algebras of block-symmetric analytic functions of bounded type

Abstract

We investigate algebras of block-symmetric analytic functions on spaces $\ell_{p}(\mathbb{C}^s)$ which are $\ell_{p}$-sums of $\mathbb{C}^{s}.$ We consider properties of algebraic bases of block-symmetric polynomials,intertwining operations on spectra of the algebras and representations of the spectra as a semigroup of analytic functions of exponential type of several variables. All invertible elements of the semigroup are described for the case $p=1.$