Bishop-Phelps-Bollobás property for positive operators when the domain is L∞
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Banach spaceOperatorBishop-Phelps-Bollobás theoremBishop-Phelps-Bollobás property
Acosta, M. D., & Soleimani-Mourchehkhorti, M. (2021). Bishop-Phelps-Bollobás property for positive operators when the domain is L∞. Bulletin of Mathematical Sciences, 11(02), 2050023. [http://dx.doi.org/10.1142/S166436072050023X]
SponsorshipJunta de Andalucia FQM-185; Spanish MINECO/FEDER grant PGC2018-093794-B-I00; IPM
We prove that the class of positive operators from L∞(μ) to Y has the Bishop-Phelps- Bollob´as property for any positive measure μ, whenever Y is a uniformly monotone Banach lattice with a weak unit. The same result also holds for the pair (c0, Y ) for any uniformly monotone Banach lattice Y. Further we show that these results are optimal in case that Y is strictly monotone.