Extensions of closed operators in Hilbert space

1980 ◽  
Vol 28 (6) ◽  
pp. 871-875 ◽  
Author(s):  
L. I. Vainerman
Keyword(s):  
Hilbert Space ◽  
Closed Operators

Regularly solvable extensions of non-self-adjoint ordinary differential operators

1984 ◽  
Vol 97 ◽  
pp. 79-95 ◽  
Author(s):  
W. D. Evans
Keyword(s):  
Hilbert Space ◽  
Weighted Space ◽  
Differential Operators ◽  
Linear Operators ◽  
Order Linear ◽  
Adjoint Pair ◽  
Closed Operators ◽  
Ordinary Differential Operators ◽  
Linear Differential ◽  
Densely Defined

SynopsisLetL0,M0be closed densely defined linear operators in a Hilbert spaceHwhich form an adjoint pair, i.e.. In this paper, we study closed operatorsSwhich satisfyand are regularly solvable in the sense of Višik. The abstract results obtained are applied to operators generated by second-order linear differential expressions in a weighted spaceL2(a, b; w).

A general version of Neubauer’s lemma and closed range almost closed operators

2019 ◽  
Vol 13 (07) ◽  
pp. 2050124
Author(s):  
Abdellah Gherbi ◽  
Sanaa Messirdi ◽  
Bekkai Messirdi
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Closed Operator ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
General Version ◽  
Closed Range ◽  
Closed Operators ◽  
Necessary And Sufficient ◽  
Closed Linear Operators

In this paper, almost closed subspaces and almost closed linear operators are described in a Hilbert space. We show Neubauer’s lemma and we give necessary and sufficient conditions for an almost closed operator to be with closed range and we exhibit sufficient conditions under which it is either closed or closable.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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