## Banach Journal of Mathematical Analysis

### 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 $w^*$-continuous operators and other related results.

#### Article information

Source
Banach J. Math. Anal., Volume 9, Number 4 (2015), 243-258.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1429286066

Digital Object Identifier
doi:10.15352/bjma/09-4-13

Mathematical Reviews number (MathSciNet)
MR3336892

Zentralblatt MATH identifier
1323.46002

#### Citation

Choi, Yun Sung; Kim, Sun Kwang; Lee, Han Ju; Martin, Miguel. On Banach spaces with the approximate hyperplane series property. Banach J. Math. Anal. 9 (2015), no. 4, 243--258. doi:10.15352/bjma/09-4-13. https://projecteuclid.org/euclid.bjma/1429286066