Almost square dual Banach spaces

2019/12/28 by Abrahamsen, Trond A., Hájek, Petr, Troyanski, Stanimir
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1912.12519

Abstract

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.

Related

• Almost square Banach spaces
• Banach spaces containing c₀ and elements in the fourth dual
• Some results on almost square Banach spaces
• Unconditional almost squareness and applications to spaces of Lipschitz\n functions
• Locally almost square Banach lattices