Banach Journal of Mathematical Analysis

The approximate hyperplane series property and related properties

María D. Acosta, Richard Martin Aron, and Francisco Javier García-Pacheco

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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.

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces

Bishop–Phelps–Bollobás property property $\beta$ equivalent renorming


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.

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