tool for the study of strong Morita equivalence. We include the following well-known technique for future reference.

\[L: H-technique\] Let $M \subseteq {{\mathcal{B}}}(H,K)$ be a TRO and let $A = {\left[ MM^* \right]^{-\|\cdot\|}}$. Let $X \subseteq {{\mathcal{B}}}(K)$ be an operator right module over $A$. Then $X \otimes_A^h M \simeq {\left[ X M \right]^{-\|\cdot\|}}$.

Let the completely contractive $A$-balanced bilinear map $X \times M \to {\left[ X M \right]^{-\|\cdot\|}}$ defined by $(x, m) \mapsto x m$. This induces a completely contractive map $$\Phi \colon X \otimes ^h_A M \mapsto {\left[ X M \right]^{-\|\cdot\|}}: x \otimes_A m \to x m.$$ Let $n_\la^* = [(n_1^\la)^*, \dots, (n_{k_\la}^\la)^*]$ be a net provided by $M$; i.e. $n_i^\la \in M$, ${\left\Vert n_\la\right\Vert} \leq 1$ and $$\lim_\la m n_\la^* n_\la = m {\text{ for all }}m\in M.$$ Fix $x_1, \dots, x_n\in X$ and $m_1, \dots, m_n \in M$. For ${\varepsilon}>0$ there exists $\la$ such that $$\begin{aligned}
\| \sum_{i=1}^n x_i \otimes m_i \| -{\varepsilon}& \leq
\| \sum_{i=1}^n x_i \otimes(m_i n_\la^* n_\la) \|
 =
\| \sum_{i=1}^n (x_i m_i n_\la^*) \otimes n_\la \| \\
& \leq
\| \sum_{i=1}^n x_i m_i n_\la^* \|
\leq
\| \sum_{i=1}^n x_i m_i \|.\end{aligned}$$ Therefore $\Phi$ is isometric. A similar argument holds for the matrix norms 