Nonmatricial Version of the Arveson–Wittstock Extension Principle, and Its Generalization

We consider the algebra $\mathcal{B}=\mathcal{B}(H)$ of bounded operators in a Hilbert space $H$, $\mathcal{B}$-bimodules, and morphisms of these bimodules into the algebra $\mathcal{B}(L\otimes H)$, where $L$ is a Hilbert space. We study the problem of extension of a morphism defined on a sub-$\mathcal{B}$-bimodule $Y\subset Z$ to $Z$. This problem is solved for Ruan bimodules.