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arXiv · 2409.14625

On norm-attaining positive operators between Banach lattices

José Lucas P. Luiz·Vinícius C. C. Miranda
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Abstract

In this paper we study the norm-attainment of positive operators between Banach lattices. By considering an absolute version of James boundaries, we prove that: If $E$ is a reflexive Banach lattice whose order is given by a basis and $F$ is a Dedekind complete Banach lattice, then every positive operator from $E$ to $F$ is compact if and only if every positive operator from $E$ to $F$ attains its norm. An analogue result considering that $E$ is reflexive and the order in $F$ is continuous and given by a basis was proven. We applied our result to study a positive version of the weak maximizing property.

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José Lucas P. Luiz, Vinícius C. C. Miranda. 2024-09-22. On norm-attaining positive operators between Banach lattices. https://arxiv.org/abs/2409.14625

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