Affiliation:
1. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
Abstract
Abstract
In these notes, we study nonlinear embeddings between Banach spaces that are also weakly sequentially continuous. In particular, our main result implies that if a Banach space $X$ coarsely (resp. uniformly) embeds into a Banach space $Y$ by a weakly sequentially continuous map, then every spreading model $(e_n)_n$ of a normalized weakly null sequence in $X$ satisfies $$ \|e_1+\ldots+e_k\|_{\overline{\delta}_Y}\lesssim\|e_1+\ldots+e_k\|_S,$$where $\overline{\delta }_Y$ is the modulus of asymptotic uniform convexity of $Y$. Among other results, we obtain Banach spaces $X$ and $Y$ so that $X$ coarsely (resp. uniformly) embeds into $Y$, but so that $X$ cannot be mapped into $Y$ by a weakly sequentially continuous coarse (resp. uniform) embedding.
Publisher
Oxford University Press (OUP)
Cited by
1 articles.
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