## Banach Journal of Mathematical Analysis

### The approximate hyperplane series property and related properties

#### Abstract

We show that the approximate hyperplane series property consequence, we obtain that the class of spaces $Y$ such that the pair $(\ell_{1},Y)$ has the Bishop–Phelps–Bollobás property for operators is stable under finite $\ell_{p}$-sums for $1\leq p\lt \infty$. We also deduce that every Banach space of dimension at least $2$ can be equivalently renormed to have the AHSp but to fail Lindenstrauss’ property $\beta$. We also show that every infinite-dimensional Banach space admitting an equivalent strictly convex norm also admits such an equivalent norm failing the AHSp.

#### Article information

Source
Banach J. Math. Anal., Volume 11, Number 2 (2017), 295-310.

Dates
Accepted: 12 May 2016
First available in Project Euclid: 19 January 2017

https://projecteuclid.org/euclid.bjma/1484816416

Digital Object Identifier
doi:10.1215/17358787-3819279

Mathematical Reviews number (MathSciNet)
MR3598746

Zentralblatt MATH identifier
06694355

#### Citation

Acosta, María D.; Aron, Richard Martin; García-Pacheco, Francisco Javier. The approximate hyperplane series property and related properties. Banach J. Math. Anal. 11 (2017), no. 2, 295--310. doi:10.1215/17358787-3819279. https://projecteuclid.org/euclid.bjma/1484816416

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