Espace de Hilbert d'op\'erateurs et Interpolation complexe

Abstract

Let $H$ be an infinite dimensional Hilbert space. We show that there exists a subspace of $B(H)$ which is isometric to $\ell_2$ and completely isometric to its antidual in the sense of the theory of operator spaces recently developed by Blecher-Paulsen and Effros-Ruan. Moreover this space is unique up to a complete isometry. We denote it by $OH$. This space has several remarkable properties in particular with respect to the complex interpolation method.