2018
DOI: 10.1090/proc/14097
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Asymptotic properties of Banach spaces and coarse quotient maps

Abstract: We give a quantitative result about asymptotic moduli of Banach spaces under coarse quotient maps. More precisely, we prove that if a Banach space Y is a coarse quotient of a subset of a Banach space X, where the coarse quotient map is coarse Lipschitz, then the (β)-modulus of X is bounded by the modulus of asymptotic uniform smoothness of Y up to some constants. In particular, if the coarse quotient map is a coarse homeomorphism, then the modulus of asymptotic uniform convexity of X is bounded by the modulus … Show more

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Cited by 2 publications
(1 citation statement)
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“…The lemma below says that co-uniformly continuous maps and co-coarsely continuous maps are "co-Lipschtiz for large distances" provided the target space is metrically convex. We refer to [1,16] for the proof. Lemma 4.2.…”
Section: Stability Of Property (β) Under Nonlinear Quotientsmentioning
confidence: 99%
“…The lemma below says that co-uniformly continuous maps and co-coarsely continuous maps are "co-Lipschtiz for large distances" provided the target space is metrically convex. We refer to [1,16] for the proof. Lemma 4.2.…”
Section: Stability Of Property (β) Under Nonlinear Quotientsmentioning
confidence: 99%