Bishop-Phelps-Bollobás property for positive operators when the domain is L∞
oleh: María D. Acosta, Maryam Soleimani-Mourchehkhorti
| Format: | Article |
|---|---|
| Diterbitkan: | World Scientific Publishing 2021-08-01 |
Deskripsi
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 (c0,Y ) for any uniformly monotone Banach lattice Y. Further we show that these results are optimal in case that Y is strictly monotone.