On the Essential Self-Adjointness of Anti-Commutative Operators

Abstract. In this article, linear operators satisfying anti-commutation relations are considered. It is proven that an anti-commutative type of the Glimm-Jaffe-Nelson commutator theorem follows. 1 Introduction and Main Theorem In this article we consider the self-adjointness of linear operators satisfying anti-commutation relations. For criteria on the self-adjointness of the symmetric operator satisfying a commuta-tion relation, there is the Glimm-Jaffe-Nelson commutator theorem. Refer to [2, 3, 4] of the original papers, and see also e.g. ([1]; Theorem 2.32, [6]; Theorem X.36). We investigate a