Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear weakly sequentially continuous embeddings between Banach
  spaces   In these notes, we study nonlinear embeddings between Banach spaces which 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.

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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn