On J-Selfadjoint Extensions of J-Symmetric Operators

1980 ◽  
Vol 79 (1) ◽  
pp. 42 ◽  
Author(s):  
Ian Knowles
Keyword(s):  
Symmetric Operators ◽  
Selfadjoint Extensions

scholarly journals Correct selfadjoint and positive extensions of nondensely defined minimal symmetric operators

2005 ◽  
Vol 2005 (7) ◽  
pp. 767-790 ◽  
Author(s):  
I. Parassidis ◽  
P. Tsekrekos
Keyword(s):  
Hilbert Space ◽  
Symmetric Operator ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Selfadjoint Extension ◽  
Symmetric Operators ◽  
Selfadjoint Extensions ◽  
Positive Extensions

LetA0be a closed, minimal symmetric operator from a Hilbert spaceℍintoℍwith domain not dense inℍ. LetA^also be a correct selfadjoint extension ofA0. The purpose of this paper is (1) to characterize, with the help ofA^, all the correct selfadjoint extensionsBofA0with domain equal toD(A^), (2) to give the solution of their corresponding problems, (3) to find sufficient conditions forBto be positive (definite) whenA^is positive (definite).

scholarly journals Scattering theory for a class of non-selfadjoint extensions of symmetric operators

2020 ◽  
pp. 194-230
Author(s):  
Kirill D. Cherednichenko ◽  
Alexander V. Kiselev ◽  
Luis O. Silva
Keyword(s):  
Scattering Theory ◽  
Symmetric Operators ◽  
Selfadjoint Extensions

scholarly journals Positive selfadjoint extensions of positive symmetric operators

1970 ◽  
Vol 22 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Tsuyoshi Ando ◽  
Katsuyoshi Nishio
Keyword(s):  
Symmetric Operators ◽  
Selfadjoint Extensions

scholarly journals On $J$-selfadjoint extensions of $J$-symmetric operators

1980 ◽  
Vol 79 (1) ◽  
pp. 42-42
Author(s):  
Ian Knowles
Keyword(s):  
Symmetric Operators ◽  
Selfadjoint Extensions

On the existence of J-selfadjoint extensions of J-symmetric operators with adjoint

1962 ◽  
Vol 15 (4) ◽  
pp. 423-425 ◽  
Author(s):  
Alberto Galindo
Keyword(s):  
Symmetric Operators ◽  
Selfadjoint Extensions

scholarly journals The theory of J-selfadjoint extensions of J-symmetric operators

1985 ◽  
Vol 57 (2) ◽  
pp. 258-274 ◽  
Author(s):  
David Race
Keyword(s):  
Symmetric Operators ◽  
Selfadjoint Extensions

Selfadjoint extensions of symmetric operators in degenerated inner product spaces

1997 ◽  
Vol 28 (3) ◽  
pp. 289-320 ◽  
Author(s):  
Michael Kaltenb�ck ◽  
Harald Woracek
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Symmetric Operators ◽  
Selfadjoint Extensions

On compressions of self-adjoint extensions of a symmetric linear relation with unequal deficiency indices

2019 ◽  
Vol 16 (4) ◽  
pp. 567-587
Author(s):  
Vadim Mogilevskii
Keyword(s):  
Hilbert Space ◽  
Boundary Conditions ◽  
Linear Relation ◽  
Deficiency Indices ◽  
Space Extension ◽  
Limit Value ◽  
Abstract Boundary ◽  
Symmetric Linear Relation ◽  
Symmetric Operators

Let $A$ be a symmetric linear relation in the Hilbert space $\gH$ with unequal deficiency indices $n_-A <n_+(A)$. A self-adjoint linear relation $\wt A\supset A$ in some Hilbert space $\wt\gH\supset \gH$ is called an (exit space) extension of $A$. We study the compressions $C (\wt A)=P_\gH\wt A\up\gH$ of extensions $\wt A=\wt A^*$. Our main result is a description of compressions $C (\wt A)$ by means of abstract boundary conditions, which are given in terms of a limit value of the Nevanlinna parameter $\tau(\l)$ from the Krein formula for generalized resolvents. We describe also all extensions $\wt A=\wt A^*$ of $A$ with the maximal symmetric compression $C (\wt A)$ and all extensions $\wt A=\wt A^*$ of the second kind in the sense of M.A. Naimark. These results generalize the recent results by A. Dijksma, H. Langer and the author obtained for symmetric operators $A$ with equal deficiency indices $n_+(A)=n_-(A)$.

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