An estimate of the Banach-Mazur distances between Hilbert spaces and Banach spaces

Abstract

We discuss a geometric property that provides tools for the estimate of the Δ2 on spaces of Rademacher functions with values on a Banach space for particular sequences of vectors. We obtain in this way a technique to study those Banach spaces that are isomorphic to Hilbert spaces. In particular, an estimate of the Banach-Mazur distance between such these spaces is obtained.