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# On a criterion of mutual adjointness for extensions of some nondensely defined operators

### Abstract

In the paper the role of initial object is played by a pair of closed linear densely defined operators $L_0$ and $M_0$, where $L_0 \subset M_0^{\ast}:= L,$ acting in Hilbert space. A criterion of mutual adjointness for some classes of the extensions of finite-dimensional (non densely defined) restrictions of $L_0$ and $M_0$ are established. The main results are based on the theory of linear relations in Hilbert spaces and are formulated in the terms of abstract boundary operators.

Key words: Hilbert space, operator, relation, extension, mutual adjointness.

### Article Information

 Title On a criterion of mutual adjointness for extensions of some nondensely defined operators Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 50-58 MathSciNet MR3242122 zbMATH 1313.47005 Milestones Received 18/09/2013 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

Iu. I. Oliiar
Department of Mathematical and Functional Analysis, Lviv Ivan Franko National University, 1 Universytetska, Lviv, 79000, Ukraine

O. G. Storozh
Department of Mathematical and Functional Analysis, Lviv Ivan Franko National University, 1 Universytetska, Lviv, 79000, Ukraine

### Citation Example

Iu. I. Oliiar and O. G. Storozh, On a criterion of mutual adjointness for extensions of some nondensely defined operators, Methods Funct. Anal. Topology 20 (2014), no. 1, 50-58.

### BibTex

@article {MFAT709,
AUTHOR = {Oliiar, Iu. I. and Storozh, O. G.},
TITLE = {On a criterion of mutual adjointness for extensions of some nondensely defined operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {1},
PAGES = {50-58},
ISSN = {1029-3531},
MRNUMBER = {MR3242122},
ZBLNUMBER = {1313.47005},
URL = {http://mfat.imath.kiev.ua/article/?id=709},
}