Polyhedrality and Decomposition-Reference-Cited by-同舟云学术

Polyhedrality and Decomposition

Published:2018-10-08 Issue:2 Volume:70 Page:409-427
ISSN:0033-5606
Container-title:The Quarterly Journal of Mathematics
language:en
Short-container-title:

Author:

Abrahamsen Trond A¹,Fonf Vladimir P²,Smith Richard J³,Troyanski Stanimir⁴⁵

Affiliation:

1. Department of Mathematics, University of Agder, Postboks 422, 4604 Kristiansand, Norway

2. Department of Mathematics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel

3. School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland

4. Institute of Mathematics and Informatics, Bulgarian Academy of Science, bl.8, acad., G. Bonchev str. 1113 Sofia, Bulgaria

5. Departamento de Matematicas, Universidad de, Murcia, Campus de Espinardo, 30100 Espinardo (Murcia), Spain

Abstract

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.

Funder

Ministry of Economy and Competitiveness

Fondo Europeo de Desarrollo Regional

Albert Ellis Institute

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/qjmath/article-pdf/70/2/409/28939689/hay050.pdf

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