Let $T:A\rightarrow A$ be unbounded operator of an abelian,unital C*-algebra $A$. Let $\lambda\in A$, if $\lambda T$ is closed operator, how about $T$ itself? Is it closed?
One of the difficulties is there may exist a sequence $a_{n}$ such that it converge, and $T(a_{n})$ is zero divisor of $\lambda$. But I can't construct a counter example.
