Strong Commutativity of Unbounded Self-adjoint Operators on a Separable Hilbert space

Abstract

The unbounded Self-adjoint operators that strongly commute on a common dense subset of their domain commute pointwise. When the operators commute pointwise on the same dense subset, there is to guarantee that they will commute strongly. By imposing some conditions, we on the operators as well as the underlying space, we get pointwise commuting unbounded operators that commute strongly.  This article shows that by suitably selecting two unbounded positive Self-adjoint operators with compact inverses we get a set of pointwise commuting self-adjoint operators that commute on common core. then prove that it strongly commutes on the same subspace.

Keywords: Unbounded operators, Self-adjoint operators, Commutative operators

DOI: 10.7176/MTM/10-8-03

Publication date: December 31^st 2020