Research examines properties of abstract Uryson operators in Riesz spaces, suggesting crucial differences in continuity types.
In this paper, we study unbounded order continuous abstract Uryson operators between Riesz spaces. We show that the space of unbounded order continuous abstract Uryson operators forms a Riesz subspace under suitable conditions. We also study several basic structural properties of such operators and analyze the relationship between order continuity and unbounded order continuity. In particular, we demonstrate that these two notions do not coincide in general and provide examples illustrating this phenomenon.
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Turan et al. (2026) studied this question.
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