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26 April 2024

» arxiv » 1907.8620

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Bishop-Phelps-Bollob'as property for positive operators when the domain is $L_infty $
M.D. Acosta ; M. Soleimani-Mourchehkhorti ;
Date:	19 Jul 2019
Abstract:	We prove that the class of positive operators from $L_infty (mu)$ to $Y$ has the Bishop-Phelps-Bollob’as property for any positive measure $mu$, 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.
Source:	arXiv, 1907.8620
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