Suppose we work in $H=l^2(\Bbb{N})$ and suppose the multiplication operator $T_f$ such that $T_f\psi=f\psi$ and $f:\Bbb{N}\rightarrow \Bbb{C}$. We denote by $B_1(H)$ the trace class of operators.
Question: I want to find a sufficient and necessary condition for $f$, such that $T_f\in B_1(H)$.
Can someone help me with this question? (This a question from a exam for Introduction to Functional analysis.)