Criteria of mutual adjointness of proper extensions of linear relations

Author Yu. I. Oliyar, O. G. Storozh,
Lviv Ivan Franko National University

Abstract 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 proper extension of $ L_0(L^{\ast})$. In the terms of abstract boundary operators 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 for mentioned above relations $L_1$ and $M_1$ are established.
Keywords extension; adjoint; Hilbert space
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Pages 71-78
Volume 40
Issue 1
Year 2013
Journal Matematychni Studii
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