Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 2 (2017), 295-310.
The approximate hyperplane series property and related properties
We show that the approximate hyperplane series property consequence, we obtain that the class of spaces such that the pair has the Bishop–Phelps–Bollobás property for operators is stable under finite -sums for . We also deduce that every Banach space of dimension at least can be equivalently renormed to have the AHSp but to fail Lindenstrauss’ property . We also show that every infinite-dimensional Banach space admitting an equivalent strictly convex norm also admits such an equivalent norm failing the AHSp.
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
Permanent link to this document
Digital Object Identifier
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
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