On the Bishop-Phelps-Bollobás property for positive functionals (Q6577488)

The authors introduce the Bishop-Phelps-Bollobás property (BPBp, for short) for positive functionals; see the paper for details. They obtain a general version of the BPBp for Banach lattices where all the elements and functionals are positive. Besides, they provide a characterization of the BPBp for positve elements and positive functionals. They also show that every finite-dimensional Banach lattice has the BPBp for positive functionals. They prove that the spaces \(L_p(\mu)\), \(C(K)\) and \(\mathcal{M}(K)\) all satisfy the BPBp for positive functionals by using Theorem~2.9, which provides a sufficient and also necessary condition for the BPBp for positive functionals. Throughout, the authors provide several examples concerning this line of study.