Symmetric polynomials on ℓ1 and the symmetric Fock space

Abstract

We consider the Hilbert space generated symmetric polynomials on the space of absolutely summing sequences. We construct an isomorphism of this space to the symmetric Fock space. This isomorphism allows us to extend combinatorial methods for investigations of tensor polynomials in the symmetric Fock space. The intertwining operator on the Hilbert space of symmetric analytic functions is investigated.