Abstract of a paper by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee and Miguel Martin
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 http://arXiv.org/abs/1407.7848
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