1-greedy renormings of Garling sequence spaces
- Albiac, F. 3
- Ansorena, J.L. 2
- Wallis, B. 1
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1
Northern Illinois University
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2
Universidad de La Rioja
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3
Universidad Pública de Navarra
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ISSN: 0021-9045
Année de publication: 2018
Volumen: 230
Pages: 13-23
Type: Article
D'autres publications dans: Journal of Approximation Theory
Résumé
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. © 2018 Elsevier Inc.