Bishop-Phelps-Bollobás property for positive operators when the domain is L∞

M. D. Acosta was supported by Junta de Andaluc ' ia grant FQM-185 and also by Spanish MINECO/FEDER grant PGC2018-093794-B-I00. M. SoleimaniMourchehkhorti was supported by a grant from 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.Junta de Andalucia FQM-185Spanish MINECO/FEDER grant PGC2018-093794-B-I00IP