The Fuglede Theorem and Some Intertwining Relations

In this paper, we show a new and classic version of the celebrated Fuglede Theorem in an unbounded setting. A related counterexample is equally presented. In the second strand of the paper, we give a pair of a closed and self-adjoint (unbounded) operators which is not intertwined by any (bounded or closed) operator except the zero operator.
Comment: 08 pages