Almost square dual Banach spaces

Almost square dual Banach spaces

We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on ℓ∞. As a consequence we get that every dual Banach space containing c0 has an equivalent almost square dual norm. Finally we characterize se...

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Veröffentlicht in:Journal of mathematical analysis and applications 2020-07, Vol.487 (2), p.124003, Article 124003
Hauptverfasser: Abrahamsen, Trond A., Hájek, Petr, Troyanski, Stanimir
Format: Artikel
Sprache:eng
Schlagworte:
Almost square Banach space
Intersection property
Locally almost square Banach space
M-ideal
Octahedral Banach space
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Zusammenfassung:We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on ℓ∞. As a consequence we get that every dual Banach space containing c0 has an equivalent almost square dual norm. Finally we characterize separable real almost square spaces in terms of their position in their fourth duals.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.124003