Quasi-selfadjoint extensions of dual pairs of linear relations

Abstract: This paper investigates quasi-selfadjoint extensions of dual pairs of linear relations in Hilbert spaces. Some properties of dual pairs of linear relations are given and an Hermitian linear relation associated with a dual pair of linear relations is introduced. Necessary and sufficient conditions for quasi-selfadjoint extensions of dual pairs of linear relations are obtained. These results extends the corresponding results for dual pairs of linear operators to dual pairs of linear relations.