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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/s3201-6067-0570-n On Extreme Extension of Positive Operators
Kusraev, A. G.
Vladikavkaz Mathematical Journal 2024. Vol. 26. Issue 2.
Abstract:
Given vector lattices \(E\), \(F\) and a positive operator \(S\) from a majorzing subspace \(D\) of \(E\) to \(F\), denote by \(\mathcal{E}(S)\) the collection of all positive extensions of \(S\) to all of \(E\). This note aims to describe the collection of extreme points of the convex set \(\mathcal{E}(T\circ S)\). It is proved, in particular, that \(\mathcal{E}(T\circ S)\) and \(T\circ\mathcal{E}(S)\) coincide and every extreme point of \(\mathcal{E}(T\circ S)\) is an extreme point of \(T\circ\mathcal{E}(S)\), whenever \(T:F\to G\) is a Maharam operator between Dedekind complete vector lattices. The proofs of the main results are based on the three ingredients: a characterization of extreme points of subdifferentials, abstract disintegration in Kantorovich spaces, and an intrinsic characterization of subdifferentials.
Keywords: vector lattice, positive operator, extreme extension, subdifferential, Maharam operator
Language: English
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![]() For citation: Kusraev, A. G. On Extreme Extension of Positive Operators, Vladikavkaz Math. J., 2024, vol. 26, no. 2, pp. 47-53. DOI 10.46698/s3201-6067-0570-n ← Contents of issue |
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