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<p>We extend the study of the class of lattice Lipschitz maps on Euclidean lattices, introduced by Arnau et al. in [<CitationRef CitationID="CR4">4</CitationRef>], to Dedekind complete Riesz spaces. We prove that the associated McShane and Whitney formulas yield the same extension result for this class of operators. Also, we discuss the problem of the diagonal representation, and that of reconstruction of an operator from its eigenvetors.</p>

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Extensions of lattice Lipschitz operators on Riesz spaces

  • 期刊论文

  • 发表日期：

    2026年4月18日

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  • Redouane Nouira

摘要

We extend the study of the class of lattice Lipschitz maps on Euclidean lattices, introduced by Arnau et al. in [4], to Dedekind complete Riesz spaces. We prove that the associated McShane and Whitney formulas yield the same extension result for this class of operators. Also, we discuss the problem of the diagonal representation, and that of reconstruction of an operator from its eigenvetors.