Examples

Let $X$ be an operator space. Then the space of completely bounded $(A_1,A_2)$- module homomorphisms between $X$ and $B(\H)$ can be identified with the dual of a module Haagerup tensor product in the following way ([Pet97, p. 67], cf. also [ER91, Cor. 4.6], [Ble92b, Prop. 2.3]):

$$\mathit{CB}_{(A_1, A_2)}(X, B(\H)) \stackrel{\mathrm{cb}}{=}(R_{\overline{\H}} \otimes_{hA_1} X \otimes_{hA_2} C_{\H})^*$$

completely isometrically.