On the nonnegativity of operator products

Seppo Hassi; Z. Sebestyén; H.S.V. de Snoo

On the nonnegativity of operator products

Seppo Hassi, Z. Sebestyén, H.S.V. de Snoo

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Abstract

A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space h is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.

Original language	English
Pages (from-to)	1 - 15
Number of pages	14
Journal	Acta mathematica hungarica
Volume	109
Issue number	1-2
Publication status	Published - Oct-2005

Keywords

nonnegative operator
symmetric operator
selfadjoint operator
product of operators
Friedrichs extension
Krein-von Neumann extension
INTEGRAL-EQUATIONS

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title = "On the nonnegativity of operator products",

abstract = "A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space h is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.",

keywords = "nonnegative operator, symmetric operator, selfadjoint operator, product of operators, Friedrichs extension, Krein-von Neumann extension, INTEGRAL-EQUATIONS",

author = "Seppo Hassi and Z. Sebesty{\'e}n and Snoo, {H.S.V. de}",

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 - On the nonnegativity of operator products

AU - Hassi, Seppo

AU - Sebestyén, Z.

AU - Snoo, H.S.V. de

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

PY - 2005/10

Y1 - 2005/10

N2 - A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space h is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.

AB - A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space h is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.

KW - nonnegative operator

KW - symmetric operator

KW - selfadjoint operator

KW - product of operators

KW - Friedrichs extension

KW - Krein-von Neumann extension

KW - INTEGRAL-EQUATIONS

M3 - Article

SN - 0236-5294

VL - 109

SP - 1

EP - 15

JO - Acta mathematica hungarica

JF - Acta mathematica hungarica

IS - 1-2

ER -

On the nonnegativity of operator products

Abstract

Keywords

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