Abstract:
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.
Key words:ideal space, partial integral operator, positive operator, integral operator.
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