Let $\displaystyle T^{2}=\mathcal{R}^{2}/2\pi\mathcal{Z}^{2}$ and consider the space $\displaystyle B(L^{2}(T^{2}))$, using the quotient topology, can we show that $\displaystyle B(L^{2}(T^{2}))$ is compact? Where B is the set of all bounded linear operators mapping elements of $\displaystyle L^{2}(T^{2})$ to itself.