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<p>It&#xa0;is known that the space of kernel operators is a&#xa0;band in the Dedekind complete vector lattice of order bounded operators acting in ideal spaces of measurable functions.In&#xa0;this paper we study the order structure of the space of partial integral operators.We&#xa0;prove that the space of all absolute partial integral operators is a&#xa0;band in the Dedekind complete vector lattice of order bounded operators acting in order dense ideal spaces of measurable functions defined on the same <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ \sigma $</EquationSource> </InlineEquation>-finite measure space.</p>

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Order Structure of the Space of Partial Integral Operators

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • B. B. Tasoev

摘要

It is known that the space of kernel operators is a band in the Dedekind complete vector lattice of order bounded operators acting in ideal spaces of measurable functions.In this paper we study the order structure of the space of partial integral operators.We prove that the space of all absolute partial integral operators is a band in the Dedekind complete vector lattice of order bounded operators acting in order dense ideal spaces of measurable functions defined on the same $ \sigma $ -finite measure space.