Let $\mathbb{X}$ be a (real or complex) Banach Space and let $\mathbb{B}(\mathbb{X})$ be the space of all bounded linear operators of $\mathbb{X}$. 

Let $\tau\_u$ be the Uniform Topology on $\mathbb{B}(\mathbb{X})$ induced by the norm on $\mathbb{B}(\mathbb{X})$and let $\tau\_{SOT}$ be the Strong Operator Topology on $\mathbb{B}(\mathbb{X})$.

When is $\mathbb{B}(\mathbb{X})$ compact with respect to $\tau\_u$ ($\tau\_{SOT}$) ?