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.

Full Text

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},
}