Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation and Schur properties for Lipschitz free spaces over
  compact metric spaces   We prove that for any separable Banach space $X$, there exists a compact
metric space which is homeomorphic to the Cantor space and whose Lipschitz-free
space contains a complemented subspace isomorphic to $X$. As a consequence we
give an example of a compact metric space which is homeomorphic to the Cantor
space and whose Lipschitz-free space fails the approximation property and we
prove that there exists an uncountable family of topologically equivalent
distances on the Cantor space whose free spaces are pairwise non isomorphic. We
also prove that the free space over a countable compact metric space has the
Schur property. These results answer questions by G. Godefroy.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: solv-int