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you used that $T^* = gS^*$. Does this mean that for a bounded and s.a. operator $f$ and a closed operator $S$ we have in general $(S\circ f)^*= f \circ S^*$?
ah thank you, but the limit that I wanted to exist for functions $f \in D(T^*)$ does not necessarily have to exist, right? I am talking about the $\lim_{x \rightarrow \pm 2 \pi} g(x)f'(x)=0$.
