2024/09/22 by Luiz, José Lucas P., Miranda, Vinícius C. C. · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2409.14625
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.