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asymptotic uniform smoothness

Journal of the Institute of Mathematics of Jussieu (1)

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ON ASYMPTOTIC UNIFORM SMOOTHNESS AND NONLINEAR GEOMETRY OF BANACH SPACES
Part of
- Normed linear spaces and Banach spaces; Banach lattices
B. M. Braga
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 1 / January 2021

Published online by Cambridge University Press:

25 March 2019, pp. 65-102

Print publication:

January 2021
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These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach–Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem.