On the linear polarization constants of finite dimensional spaces

Abstract

We study the linear polarization constants of finite dimensional Banach spaces. We obtain the correct asymptotic behaviour of these constants for the spaces ld p : they behave as p√ d if 1 ≤ p < 2. and as √ d if 2 ≤ p < ∞. For p = ∞ we get the asymptotic behaviour up to a logarithmic factor.