On Self-Adjoint Linear Relations

A linear operator on a Hilbert space , in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can shown that symmetry could omitted by using criterion for graph and adjoint graph. Namely, S is densely defined closed if only . In more general setup, we consider relations instead operators prove this situation similar result holds. We give necessary sufficient condition relation self-adjoint.