Rectangular matrices

For a matricially normed space $X$, the spaces $M_{n,m}(X)=M_{n,m}\otimes X$ of $n\times m$-matrices over $X$ are normed by adding zeros so that one obtains a square matrix, no matter of which size.

Then

$$M_{n,m}(B(\H))=B(\H^m,\H^n)$$

holds isometrically.