科研之友
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摘要
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 (beta)-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 of asymptotic uniform smoothness of Y up to some constants.
- 出版日期2018-11
