6533b832fe1ef96bd129ada7

RESEARCH PRODUCT

Polyhedrality and decomposition

Richard J. SmithTrond A. AbrahamsenStanimir TroyanskiStanimir TroyanskiVladimir P. Fonf

subject

Unit spherePure mathematicsMathematics::Functional AnalysisBasis (linear algebra)General Mathematics010102 general mathematicsBanach space01 natural sciencesSchauder basisTask (project management)Functional Analysis (math.FA)Mathematics - Functional Analysis0103 physical sciencesDecomposition (computer science)FOS: Mathematics46B03 46B20 46B26Uncountable set010307 mathematical physics0101 mathematicsMathematics

description

Abstract The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The hypotheses of both results are based on decomposing the unit sphere of a Banach space into countably many pieces, such that each one satisfies certain properties. Some examples of spaces having equivalent polyhedral norms are given.

yearjournalcountryeditionlanguage
2018-04-17
https://dx.doi.org/10.48550/arxiv.1804.06348