Polyhedrality and decomposition
| Autor: | Richard J. Smith, Trond A. Abrahamsen, Stanimir Troyanski, Vladimir P. Fonf |
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| Rok vydání: | 2018 |
| Předmět: |
Unit sphere
Pure mathematics Mathematics::Functional Analysis Basis (linear algebra) General Mathematics 010102 general mathematics Banach space 01 natural sciences Schauder basis Task (project management) Functional Analysis (math.FA) Mathematics - Functional Analysis 0103 physical sciences Decomposition (computer science) FOS: Mathematics 46B03 46B20 46B26 Uncountable set 010307 mathematical physics 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1804.06348 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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