Let $c_0$ denote the set of all complex sequences that converge to zero.
We can show that $c_0$ is a $C^*$-algebra with the $*$-involution defined as complex conjugate and norm $$\|x\| = \max_j |x_j|$$ for every $x \in c_0$.
I know that every $C^*$-algebra is $*$-isomorphic to a $C^*$-subalgebra of $B(H)$ for some Hilbert space $H$.
How do I go about finding this $C^*$-subalgebra of $B(H)$ for $c_0$?
Any help pointing me in the right direction would be much appreciated.