Bishop-Phelps-Bollobás property for positive operators when the domain is L∞ Acosta Vigil, María Dolores Soleimani-Mourchehkhorti, Maryam Banach space Operator Bishop-Phelps-Bollobás theorem Bishop-Phelps-Bollobás property 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. 2021-10-13T07:46:43Z 2021-10-13T07:46:43Z 2020-12-26 info:eu-repo/semantics/article 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] http://hdl.handle.net/10481/70815 10.1142/S166436072050023X eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España World Scientific