Let $\displaystyle K=K(H)$ with $\displaystyle H$ a infinite dimensional, separable Hilbert space. Let $\displaystyle (e_n)^{\infty}_{n=1}$ be an orthonormal basis for $\displaystyle H$. Let $\displaystyle e_{ij}$ be an operator in $\displaystyle B(H)$ defined by $\displaystyle e_{ij}(x)=\langle x,e_j\rangle e_i$

set $\displaystyle p_n=\sum^{n}_{j=1}e_{jj}$ now show that the following map is a *-isomorphism (bijective *-homomorphism)

$\displaystyle \psi_{n}:M_n(A)\rightarrow p_nKp_n\otimes A, (a_{r,s})\mapsto\sum^{n}_{i,j=1}e_{ij}\otimes a_{r,s}$