A note on ball-covering property of Banach spaces

摘要: Abstract By a ball-covering B of Banach space X , we mean that is collection open (or closed) balls off the origin whose union contains unit sphere S ; and said to have property (BCP) provided it admits by countably many balls. In this note give natural example showing not inherited its subspaces; present sharp quantitative version recent Fonf Zanco renorming result saying if dual ∗ w separable, then for every e > 0 there exist ( 1 + )-equivalent norm on an R such in new radius . Namely, show = ) can be taken arbitrarily close / l [ ] corresponding cannot equal This gives order magnitude as →