A sharp operator version of the Bishop-Phelps theorem for operators from l_1 to CL-spaces

摘要

Acosta et al. in 2008 gave a characterization of a Banach space Y (called an approximate hyperplane series property, or AHSP for short) guaranteeing exactly that a quantitative version of the Bishop-Phelps theorem holds for bounded operators from l_1 to the space Y. In this note, we give two new examples of spaces having the AHSP: the almost CL-spaces and the class of Banach spaces Y whose dual Y* is uniformly strongly subdifferentiable on some boundary of Y. We then calculate the precise parameters associated to almost CL-spaces.