Deficiency Indices of Some Classes of Unbounded H -Operators

Abstract

In this paper we define the deficiency indices of a closed symmetric right H-linear operator and formulate a general theory of deficiency indices in a right quaternionic Hilbert space. This study provides a necessary and sufficient condition in terms of deficiency indices and in terms of S-spectrum, parallel to their complex counterparts, for a symmetric right H-linear operators to be self-adjoint.