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<p>Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {L}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">L</mi> </math></EquationSource> </InlineEquation> be a Dedekind complete unital <i>f</i>-algebra. We prove the Riesz-Kantorovich formulas for order bounded <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {L}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">L</mi> </math></EquationSource> </InlineEquation>-module homomorphisms from a directed partially ordered <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathbb {L}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">L</mi> </math></EquationSource> </InlineEquation>-module with the Riesz Decomposition Property into a Dedekind complete <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbb {L}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">L</mi> </math></EquationSource> </InlineEquation>-vector lattice satisfying an additional mild condition.</p>

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The Riesz-Kantorovich formulas for \(\mathbb {L}\)-vector lattices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月3日

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  • Tomas Chamberlain,
  • Marten Wortel

摘要

Let \(\mathbb {L}\) L be a Dedekind complete unital f-algebra. We prove the Riesz-Kantorovich formulas for order bounded \(\mathbb {L}\) L -module homomorphisms from a directed partially ordered \(\mathbb {L}\) L -module with the Riesz Decomposition Property into a Dedekind complete \(\mathbb {L}\) L -vector lattice satisfying an additional mild condition.