Abstract
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.
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Dedicated to Prof. Romulus Cristescu on his 80th birthday
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Dăneţ, N., Dăneţ, RM. Existence and extensions of positive linear operators. Positivity 13, 89–106 (2009). https://doi.org/10.1007/s11117-008-2220-0
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DOI: https://doi.org/10.1007/s11117-008-2220-0