Existence and extensions of positive linear operators

In this paper we develop some unified methods, based on the technique of the auxiliary sublinear operator, for obtaining extensions of positive linear operators. In the first part, a version of the Mazur-Orlicz theorem for ordered vector spaces is presented and then this theorem is used in diverse a...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 13; no. 1; pp. 89 - 106
Main Authors: DANET, Nicolae, DANET, Rodica-Mihaela
Format: Journal Article
Language:English
Published: Basel Birkhäuser-Verlag 01.02.2009
Springer
Springer Nature B.V
Subjects:
Calculus of Variations and Optimal Control; Optimization
Decision theory
Econometrics
Exact sciences and technology
Fourier Analysis
Functional analysis
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Probability and statistics
Sciences and techniques of general use
Statistics
Studies
Theorems
Vector space
extensions of positive linear operators
Secondary 47B60, 47B65
linear operators on ordered vector spaces
Primary 46A22
Mazur-Orlicz theorem
sublinear operators
Necessary condition
Sufficient condition
Vector space
Mathematical analysis
Orlicz space
Monotone operator
Linear operator
Ordered space
Operator theory
Positive operator
Functional theory
Inequality
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary:In this paper we develop some unified methods, based on the technique of the auxiliary sublinear operator, for obtaining extensions of positive linear operators. In the first part, a version of the Mazur-Orlicz theorem for ordered vector spaces is presented and then this theorem is used in diverse applications: decomposition theorems for operators and functionals, minimax theory and extensions of positive linear operators. In the second part, we give a general sufficient condition (an implication between two inequalities) for the existence of a monotone sublinear operator and of a positive linear operator. Some particular cases in which this condition becomes necessary are also studied.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-008-2220-0