Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415137 | Journal of Functional Analysis | 2014 | 18 Pages |
Abstract
The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable decompositions, either of the unit sphere SX or of certain subsets of the dual ball BXâ of a given Banach space X. The sufficient conditions of Theorem 4 are shown to be necessary in the separable case. Using Theorem 7, we can unify two known results regarding the polyhedral renorming of certain C(K) spaces, and spaces having an (uncountable) unconditional basis. New examples of spaces having equivalent polyhedral norms are given in the final section.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
V. Fonf, A.J. Pallarés, R.J. Smith, S. Troyanski,