Hilbert spaces of symmetric analytic functions on $\ell_1$

О.М. Holubchak

Hilbert spaces of symmetric analytic functions on $\ell_1$

Authors

О.М. Holubchak Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine

Keywords:

symmetric analytical functions on Banach spaces, Hilbert spaces of analytic functions

Published online: 2011-06-30

Abstract

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.