Let $\mathcal{K}(\mathcal{H})$ be the C*-algebra of compact operators on a Hilbert space $\mathcal{H}$. I am interested in the ($c_0$-)sum

$A=\sum \mathcal{K}(\mathcal{H})$

of countably many copies of this algebra.

Is it *-isomorphic to $\mathcal{K}(\mathcal{H})$ itself? Or at least as a Banach space?