Additional conditions of self-adjoint operator to be applied self-adjoint linear relation on a Hilbert space

Abstract

Let ℌ is a Hilbert space over field real number ℝ. An operator T on ℌ is a function from ℌ to ℌ. A Self-adjoint operator is an operator that satisfies T = T*. Furthermore, a linear relation ε on ℌ is the set of pairs of elements w and x with w,x ∈ ℌ. A self-adjoint linear relation is a relation that meets ε = ε*. Some properties of a Self-adjoint operator on ℌ is not applicable in self-adjoint linear relation. This paper aims to determine the properties of a self-adjoint linear relation based on linear operators.