1-greedy renormings of Garling sequence spaces

JOURNAL OF APPROXIMATION THEORY

卷:230

Article

Albiac, Fernando¹  Ansorena, Jose L.²  Wallis, Ben³ 

[1] Univ Publ Navarra, Math Dept, Campus Arrosadia, Pamplona 31006, Spain

[2] Univ La Rioja, Dept Math & Comp Sci, Logrono 26004, Spain

[3] Northern Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA

关键词: Subsymmetric basis;    Greedy basis;    Renorming;    Property (A);    Sequence spaces;    Superreflexivity;    Uniform convexity;   

DOI  :  10.1016/j.jat.2018.03.002

来源: Elsevier

【 摘 要 】

We show that all Garling sequence spaces admit a renorming with respect to which their standard unit vector basis is 1-greedy. We also discuss some additional properties of these Banach spaces related to uniform convexity and superreflexivity. In particular, our approach to the study of the superreflexivity of Garling sequence spaces provides an example of how essentially non-linear tools from greedy approximation can be used to shed light on the linear structure of these spaces. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free