I am trying to solve this problem. Let $K:[0,1]\times [0,1]\rightarrow C$ be continuous function and operator $T_k:C[0,1]\rightarrow C[0,1]$ defined as $T_K(f)(s) = \int_0^1 K(t,s) f(t){\rm d}t$, where $K(s,t)=\overline{K(t,s)}$. Is this operator compact?
Thank you!