Criteria of mutual adjointness of proper extensions of linear relations

Author Yu. I. Oliyar, O. G. Storozh
aruy14@ukr.net, storog@ukr.net
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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