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.
"The approximate hyperplane series property and related properties." Banach J. Math. Anal. 11 (2) 295 - 310, April 2017. https://doi.org/10.1215/17358787-3819279