Partial integral representation of linear positive operators

In this talk, we consider partial integral operators acting in ideal spaces of measurable real-valued functions defined on the product of measurable spaces with $\sigma$-finite measures. We provide a theorem that establishes a criterion for the partial integral representability of positive homogeneous operators. This theorem serves as an analogue of Bukhvalov’s criterion for the integral representability of linear operators acting in ideal spaces of measurable real-valued functions defined on measurable spaces with σ-finite measures.