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

Let is a Hilbert space over field real number . An operator T on is a function from to . A Self-adjoint operator is an operator that satisfies T = T *. Furthermore, a linear relation ε on is the set of pairs of elements w and x with w,x ∈ . A self-adjoint linear relation is a relation that meets ε = ε*. Some properties of a Self-adjoint operator on 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.