Bishop-Phelps-Bollobás property for positive operators between classical Banach spaces

Abstract

We prove that the class of positive operators from $L_{\infty }(\mu )$ to $L_1(\nu )$ has the Bishop-Phelps-Bollobás property for any positive measures $\mu$ and $\nu$. The same result also holds for the pair $(c_0,{\ell }_1)$. We also provide an example showing that not every pair of Banach lattices satisfies the Bishop-Phelps-Bollobás property for positive operators.

13 pages