On Banach spaces with the approximate hyperplane series property

Abstract

We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollobás version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of $w^{\ast }$-continuous operators and other related results.

12 pages

Cited by in corpus (2)

• The Bishop-Phelps-Bollobás and approximate hyperplane series properties
• Stability results of properties related to the Bishop-Phelps-Bollobás property for operators