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Positive selfadjoint extensions of positive symmetric operators

Tsuyoshi Ando, +1 more
- 01 Jan 1970 - 
- Vol. 22, Iss: 1, pp 65-75
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This article is published in Tohoku Mathematical Journal.The article was published on 1970-01-01 and is currently open access. It has received 137 citations till now. The article focuses on the topics: Elementary symmetric polynomial & Complete homogeneous symmetric polynomial.

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Operators on anti-dual pairs: self-adjoint extensions and the Strong Parrott Theorem

Zsigmond Tarcsay, +1 more
- 05 Feb 2020 - 
TL;DR: In this paper, the authors developed an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs, which can be applied for structures not carrying a Hilbert space structure or a normable topology.

The Proper Dissipative Extensions of a Dual Pair

Christoph Fischbacher, +2 more
TL;DR: In this paper, a method of determining the proper dissipative extensions of a dual pair of operators on a Hilbert space is presented. But the stability of the numerical range of the different extensions is not investigated.
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Antitonicity of the inverse for selfadjoint matrices, operators, and relations

Jussi Behrndt, +3 more
- 22 Mar 2014 - 
TL;DR: In this article, the authors extend the self-adjointness results for matrices to selfadjoint relations in separable Hilbert spaces and show that the validity of the inequalities is characterized in terms of the inertia of the relations.
Journal ArticleDOI

Extensions of dissipative operators with closable imaginary part

Christoph Fischbacher
- 01 Jan 2021 - 
TL;DR: In this article, a necessary and sufficient condition for an extension of a dissipative operator to still be dissipative was given, and the conditions for maximally accretive extensions of strictly positive symmetric operators and maximally dissipative extensions of a highly singular first-order operator on the interval were described.
Book ChapterDOI

Non-negative Self-adjoint Extensions in Rigged Hilbert Space

Yury Arlinskiĭ, +1 more
TL;DR: In this article, the authors studied extremal non-negative self-adjoint bi-extensions of a symmetric operator A with the exit in the rigged Hilbert space constructed by means of the adjoint operator A* (biextensions) and provided criteria of existence and descriptions of such extensions and associated closed forms.
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Book

Functional analysis

Frigyes Riesz
Journal ArticleDOI

Theory of Linear Operators in Hilbert Space. By N. I. Akhiezer and I. M. Glazman. Vol. 1, 50s. Vol. 2, 60a. 1964. (Constable)

F. Smithies
- 01 Dec 1966 -