and the proof is complete.

Strong Morita equivalence for operator algebras
-----------------------------------------------

There is a rich Morita theory for C\*-algebras produced by Rieffel [@Rie74], Brown [@Bro77] and Brown-Green-Rieffel [@BGR77]. Morita theory extends in various ways to nonselfadjoint operator algebras with the most influential being the direction of Blecher-Muhly-Paulsen [@BMP00] for algebras that admit an approximate unit. For the sake of completeness we include a short description.

Suppose that ${{\mathcal{A}}}$ and ${{\mathcal{B}}}$ are operator algebras with c.a.i.’s and let the bimodules ${}_{{\mathcal{A}}}M_{{\mathcal{B}}}$ and ${}_{{\mathcal{B}}}N_{{\mathcal{A}}}$. Following [@BMP00 Definition 3.1], a *Morita context* is a system $({{\mathcal{A}}},{{\mathcal{B}}}, M, N, (\cdot,\cdot), [\cdot,\cdot])$ where the maps $$(\cdot,\cdot) \colon M \times N \to {{\mathcal{A}}}{\quad\text{and}\quad}[\cdot,\cdot] \colon N \times M \to {{\mathcal{B}}}$$ are completely bounded, bilinear and balanced satisfying the following three properties:

1.  For all $m_1, m_2 \in M$ and $n_1, n_2 \in N$ we have that $(m_1, n_1) m_2 = m_1 [n_1, m_2]$ and $[n_1, m_1] n_2 = n_1 (m_1, n_2)$;

2.  The map from $M \otimes^h N$ to ${{\mathcal{A}}}$ induced by $(\cdot, \cdot)$ is a complete quotient map onto ${{\mathcal{A}}}$;

3.  The map from $N \otimes^h M$ to ${{\mathcal{B}}}$ induced by $[\cdot, \cdot]$ is a complete quotient map onto ${{\mathcal{B}}}$.

If such a system exists 