Sur les op\'erateurs factorisables par $OH$

Abstract

Let $H,K$ be Hilbert spaces. Let $E \subset B(H)$ and $F \subset B(K)$ be operator spaces in the sense of [1,2]. We study the operators $u : E \to F$ which admit a factorization $E \to OH \to F$ with completely bounded maps through the operator Hilbert space $OH$ which we have introduced and studied in a recent note. We give a characterization of these operators which allows to develop a theory entirely analogous to that of operators between Banach spaces which can be factored through a Hilbert space.