Open Access
April 2017 The approximate hyperplane series property and related properties
María D. Acosta, Richard Martin Aron, Francisco Javier García-Pacheco
Banach J. Math. Anal. 11(2): 295-310 (April 2017). DOI: 10.1215/17358787-3819279


We show that the approximate hyperplane series property consequence, we obtain that the class of spaces Y such that the pair (1,Y) has the Bishop–Phelps–Bollobás property for operators is stable under finite p-sums for 1p<. 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 β. We also show that every infinite-dimensional Banach space admitting an equivalent strictly convex norm also admits such an equivalent norm failing the AHSp.


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María D. Acosta. Richard Martin Aron. Francisco Javier García-Pacheco. "The approximate hyperplane series property and related properties." Banach J. Math. Anal. 11 (2) 295 - 310, April 2017.


Received: 15 March 2016; Accepted: 12 May 2016; Published: April 2017
First available in Project Euclid: 19 January 2017

zbMATH: 06694355
MathSciNet: MR3598746
Digital Object Identifier: 10.1215/17358787-3819279

Primary: 46B20
Secondary: 46B03

Keywords: Bishop–Phelps–Bollobás property , equivalent renorming , property $\beta$

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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