Hilbert spaces of symmetric analytical functions on ℓ1\ell_{1}

We consider completions of the space of symmetric polynomials on $\ell_{1}$ with respect to some Hilbert norm and investigate conditions under which the obtained spaces consist of analytic functions with domains in $\ell_{1}$. Some connections with abstract Fock spaces are established

On bidual bases in the space of symmetric analytic functions on ell1ell_{1}

We consider a special Hilbert space of symmetric analytic functions on$ell_1$ and construct a pair of bidual bases of polynomials.}{Hilbert space, symmetricanalytic functions, bidual base