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

We prove that the class of positive operators from L ∞ ( μ ) to Y has the Bishop-Phelps-Bollobás 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 ( c 0 , Y ) for any uniformly monotone Banach lattice Y ....

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Bibliographic Details
Published in:Bulletin of mathematical sciences 2021-08, Vol.11 (2), p.2050023-2050023-16
Main Authors: Acosta, María D., Soleimani-Mourchehkhorti, Maryam
Format: Article
Language:English
Subjects:
banach space
bishop-phelps-bollobás property
bishop-phelps-bollobás theorem
operator
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Summary:We prove that the class of positive operators from L ∞ ( μ ) to Y has the Bishop-Phelps-Bollobás 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 ( c 0 , Y ) for any uniformly monotone Banach lattice Y . Further we show that these results are optimal in case that Y is strictly monotone.
ISSN:1664-3607
1664-3615
DOI:10.1142/S166436072050023X