Bishop-Phelps-Bollob\'as property for positive operators when the domain is $L_\infty $

M. D. Acosta; M. Soleimani-Mourchehkhorti

doi:10.1142/S166436072050023X

Bishop-Phelps-Bollob\'as property for positive operators when the domain is $L_\infty $

Functional Analysis 2021-06-14 v1

Authors: M. D. Acosta , M. Soleimani-Mourchehkhorti

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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.

Keywords

bishop-phelps-bollobas property positive operators banach lattice uniformly monotone l_infinity c_0

Cite

@article{arxiv.1907.08620,
  title  = {Bishop-Phelps-Bollob\'as property for positive operators when the domain is $L_\infty $},
  author = {M. D. Acosta and M. Soleimani-Mourchehkhorti},
  journal= {arXiv preprint arXiv:1907.08620},
  year   = {2021}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:1905.12972

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