Abstract
We show that if a continuous bump function on a Banach space X locally depends on finitely many elements of a set F in X*, then the norm closed linear span of F equals to X*. Some corollaries for Markuševič bases and Asplund spaces are derived.
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. Classical Banach Spaces I
2. Smooth Norms that Depend Locally on Finitely many Coordinates
3. Norms locally dependent on finitely many coordinates;Pechanec;An. Acad. Brasil. Ciênc.,1981
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Smooth and Polyhedral Norms via Fundamental Biorthogonal Systems;International Mathematics Research Notices;2022-08-04
2. Topology, isomorphic smoothness and polyhedrality in Banach spaces;Topology and its Applications;2019-10
3. Banach Space Theory;CMS Books in Mathematics;2011
4. Higher Order Smoothness;CMS Books in Mathematics;2010-10-18
5. LFC bumps on separable Banach spaces;Journal of Mathematical Analysis and Applications;2010-05