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*-continuous operators and other related results.
Original language | English |
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Pages (from-to) | 243-258 |
Number of pages | 16 |
Journal | Banach Journal of Mathematical Analysis |
Volume | 9 |
Issue number | 4 |
DOIs | |
State | Published - 2015 |
Keywords
- Approximation
- Banach space
- Bishop-Phelps-Bollobás theorem
- Norm-attaining operators