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 Eurasian Math. J., 2016, Volume 7, Number 3, Pages 17–32 (Mi emj230)

Normal extensions of linear operators

B. N. Biyarov

Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpayev St., 010008 Astana, Kazakhstan

Abstract: Let $L_0$ be a densely defined minimal linear operator in a Hilbert space $H$. We prove that if there exists at least one correct extension $L_S$ of $L_0$ with the property $D(L_S ) = D(L^*_S )$, then we can describe all correct extensions $L$ with the property $D(L) = D(L^*)$. We also prove that if $L_0$ is formally normal and there exists at least one correct normal extension $L_N$, then we can describe all correct normal extensions $L$ of $L_0$. As an example, the Cauchy–Riemann operator is considered.

Keywords and phrases: formally normal operator, normal operator, correct restriction, correct extension.

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MSC: 47Axx, 47A05; 47B15
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Citation: B. N. Biyarov, “Normal extensions of linear operators”, Eurasian Math. J., 7:3 (2016), 17–32

Citation in format AMSBIB
\Bibitem{Biy16} \by B.~N.~Biyarov \paper Normal extensions of linear operators \jour Eurasian Math. J. \yr 2016 \vol 7 \issue 3 \pages 17--32 \mathnet{http://mi.mathnet.ru/emj230} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3581181} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000391008000003} 

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This publication is cited in the following articles:
1. M. E. Akhymbek, M. A. Sadybekov, “Correct restrictions of first-order functional-differential equation”, International Conference Functional Analysis in Interdisciplinary Applications FAIA 2017, AIP Conf. Proc., 1880, eds. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 050014
2. E. Providas, I. N. Parasidis, “On the solution of some higher-order integro-differential equations of special form”, Vestn. SamU. Estestvennonauchn. ser., 26:1 (2020), 14–22
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