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ON ASYMPTOTIC UNIFORM SMOOTHNESS AND NONLINEAR GEOMETRY OF BANACH SPACES

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  25 March 2019

B. M. Braga
B. M. Braga*
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele St., Toronto, Ontario, M3J IP3, Canada ([email protected]) https://sites.google.com/site/demendoncabraga
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Abstract

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.

Keywords

coarse Lipschitz geometryasymptotic uniform smoothnessweak sequential continuityBanach–Saks properties

MSC classification

Primary: 46B80: Nonlinear classification of Banach spaces; nonlinear quotients
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 1 , January 2021 , pp. 65 - 102
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Copyright
© Cambridge University Press 2019

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Footnotes

The author is supported by York Science Research Fellowship.

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