This is an announcement for the paper “On the linear polarization constants of finite dimensional spaces” by Daniel Carandohttps://arxiv.org/find/math/1/au:+Carando_D/0/1/0/all/0/1, Damián Pinascohttps://arxiv.org/find/math/1/au:+Pinasco_D/0/1/0/all/0/1, Jorge Tomás Rodríguezhttps://arxiv.org/find/math/1/au:+Rodriguez_J/0/1/0/all/0/1.
Abstract: We study the linear polarization constants of finite dimensional Banach spaces. We obtain the correct asymptotic behaviour of these constants for the spaces $\ell_p^d$: they behave as $d^{1/p}$ if $1\leq p\leq 2$ and as $\sqrt{d}$ if $2\leq p<\infty$. For $p=\infty$ we get the asymptotic behavior up to a logarithmic factor.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1703.06316