Homomorphisms of the algebra of symmetric analytic functions on $\ell_1$

Abstract

The algebra $\mathcal{H}_{bs}(\ell_1)$ of symmetric analytic functions of bounded type is investigated. In particular, we study continuity of some homomorphisms of the algebra of symmetric polynomials on $\ell_p$ and composition operators of the algebra of symmetric analytic functions. The paper contains several open questions.

Keywords

• polynomials and analytic functions on banach spaces
• symmetric polynomials
• spectra of algebras