Criteria of mutual adjointness of proper extensions of linear relations - O. G. Storozh; Yu. I. Oliyar (Математичні Студії, 2013)
In the paper the role of {an} initial object is played by a~couple$(L,L_0)$ of closed linear relations in a~Hilbert space $H$,such that $L_0 subset L$. Each closed linear relation $L_1(M_1)$such that $L_0 subset L_1 subset L$ (respectively $L^{ast}subset M_1 subset L_0^{ast} $) is said to be a~properextension of $ L_0(L^{ast})$. In the terms of abstract boundaryoperators i.e. bounded linear operator $U(V)$ acting from $L(M)$ to$G$ ($G$ is an auxiliary Hilbert space) such that {the} null space of$U(V)$ contains $L_0(L^{ast})$, {criteria}~of mutual adjointness formentioned above relations $L_1$ and $M_1$ are established.