Geodesic
On partial integral representation of linear positive operators
Vladikavkazskij matematičeskij žurnal, Tome 27 (2025) no. 1, pp. 101-111

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In this paper, we obtain a criterion for partial integral representability of positive $L^\infty$-homogeneous operators acting in ideal spaces of measurable real functions defined on the product of measurable spaces with $\sigma$-finite measures. The result obtained is a counterpart of Bukhvalov's criterion for integral representability of linear operators acting in ideal spaces of measurable real functions defined on measurable spaces with $\sigma$-finite measures. Note that under certain conditions, the above-mentioned Bukhvalov criterion can be derived from the result obtained in this paper. Consequently, the result obtained is a generalization of Bukhvalov's criterion. The main tools of this study are the above-mentioned Bukhvalov criterion and the methods of vector lattice theory. 
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P. R. Orinbaev; B. B. Tasoev. On partial integral representation of linear positive operators. Vladikavkazskij matematičeskij žurnal, Tome 27 (2025) no. 1, pp. 101-111. http://geodesic.mathdoc.fr/item/VMJ_2025_27_1_a7/