CONDITIONS IMPLYING COMMUTATIVITY OF UNBOUNDED SELF-ADJOINT OPERATORS AND RELATED TOPICS

摘要

Let B be a bounded self-adjoint operator and let A be a nonnegative self-adjoint unbounded operator. It is shown that if BA is normal, it must be self-adjoint and so must be AB. Commutativity is necessary and sufficient for this result. If AB is normal, it must be self-adjoint and BA is essentially self-adjoint. Although the two problems seem to be alike, two different and quite interesting approaches are used to tackle them.