Homomorphisms of the algebra of symmetric analytic functions on ℓ1\ell_1

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

SYMMETRIC POLYNOMIALS AND HOLOMORPHIC FUNCTIONS ON INFINITE DIMENSIONAL SPACES

A survey of general results about spectra of uniform algebras of symmetricholomorphic functions and algebras of symmetric analytic functions of bounded type onBanach spaces is given.</span

Spectra of algebras of symmetric and subsymmetric analytic functions

Algebras of symmetric and subsymmetric analytic functions ofbounded type on spaces $L_1[0,infty)cap L_{infty}[0,infty)$ and$L_{infty}[0,1]$ and their spectra are investigated