An application of the Putnam-Fuglede theorem to normal products of self-adjoint operators

Abstract

Abstract. We prove that if we have two self-adjoint operators (bounded or not) and if their product is normal, then it is self-adjoint provided a certain condition is satisfied.

Unbounded products of operators and connections to Dirac-type operators

“…Let Because as a nonnegative self-adjoint operator |B| satisfies the spectral condition that σ(|B|)) ∩ σ(−|B|) = {0} of Theorem 6 of [21], we know that |A||B| is normal iff it is self-adjoint.…”

On the Adjoint and the Closure of the Sum of Two Unbounded Operators

“…A similar operator (in fact −i(|x| f ) ′ ) appeared in [19], in a different setting, where the reader may find more details. Then The following theorem generalizes the previous proposition to general densely defined A and B.…”

Generalizations of Kaplansky Theorem for some (p,k)-Quasihyponormal Operators

“…In [18,Theorem 3] The study of operators satisfying Kaplansky theorem is of significant interest and is currently being done by a number of mathematicians around the world.Some developments toward this subject have been done in [6,10,12,15,16,17] and the references therein.…”