A characterization of semibounded selfadjoint operators

Seppo Hassi; M Kaltenback; H DeSnoo

A characterization of semibounded selfadjoint operators

Seppo Hassi, M Kaltenback, H DeSnoo

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Abstract

For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when S is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator A is semibounded if and only if each one-dimensional restriction of A has a generalized Friedrichs extension.

Original language	English
Pages (from-to)	2681-2692
Number of pages	12
Journal	Proceedings of the american mathematical society
Volume	125
Issue number	9
Publication status	Published - Sep-1997

Keywords

Nevanlinna function
Q-function
Friedrichs extension
selfadjoint extension
symmetric operator

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title = "A characterization of semibounded selfadjoint operators",

abstract = "For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when S is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator A is semibounded if and only if each one-dimensional restriction of A has a generalized Friedrichs extension.",

keywords = "Nevanlinna function, Q-function, Friedrichs extension, selfadjoint extension, symmetric operator",

author = "Seppo Hassi and M Kaltenback and H DeSnoo",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)",

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T1 - A characterization of semibounded selfadjoint operators

AU - Hassi, Seppo

AU - Kaltenback, M

AU - DeSnoo, H

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1997/9

Y1 - 1997/9

N2 - For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when S is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator A is semibounded if and only if each one-dimensional restriction of A has a generalized Friedrichs extension.

AB - For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when S is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator A is semibounded if and only if each one-dimensional restriction of A has a generalized Friedrichs extension.

KW - Nevanlinna function

KW - Q-function

KW - Friedrichs extension

KW - selfadjoint extension

KW - symmetric operator

M3 - Article

VL - 125

SP - 2681

EP - 2692

JO - Proceedings of the american mathematical society

JF - Proceedings of the american mathematical society

SN - 0002-9939

IS - 9

ER -