This is an announcement for the paper "On Banach spaces with the approximate hyperplane series property" by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee and Miguel Martin.
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-Bollob'{a}s 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.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Remarks: 12 pages
Submitted from: hanjulee@dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.7848
or