UNIVERSALITY, COMPLEXITY AND ASYMPTOTICALLY UNIFORMLY SMOOTH BANACH SPACES

R Causey , Gilles Lancien (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

For 1 < p ≤ ∞, we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent p-asymptotically uniformly smooth norm. We prove that this class is analytic complete in the class of separable Banach spaces. These results extend previous works by Kalton, Werner and Kurka in the case p = ∞.

Domaines: Mathématiques [math]

R Causey, Gilles Lancien. UNIVERSALITY, COMPLEXITY AND ASYMPTOTICALLY UNIFORMLY SMOOTH BANACH SPACES. Commentationes Mathematicae Universitatis Carolinae, 2023, 64 (1), pp.1-17. ⟨hal-03618975v2⟩