Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Joint spreading models and uniform approximation of bounded operators   We investigate the following property for Banach spaces. A Banach space $X$
satisfies the Uniform Approximation on Large Subspaces (UALS) if there exists
$C>0$ with the following property: for any $A\in\mathcal{L}(X)$ and convex
compact subset $W$ of $\mathcal{L}(X)$ for which there exists $\varepsilon>0$
such that for every $x\in X$ there exists $B\in W$ with
$\|A(x)-B(x)\|\le\varepsilon\|x\|$, there exists a subspace $Y$ of $X$ of
finite codimension and a $B\in W$ with $\|(A-B)|_Y\|_{\mathcal{L}(Y,X)}\leq
C\varepsilon$. We prove that a class of separable Banach spaces including
$\ell_p$, for $1\le p< \infty$, and $C(K)$, for $K$ countable and compact,
satisfy the UALS. On the other hand every $L_p[0,1]$, for $1\le p\le \infty$
and $p\neq2$, fails the property and the same holds for $C(K)$, where $K$ is an
uncountable metrizable compact space. Our sufficient conditions for UALS are
based on joint spreading models, a multidimensional extension of the classical
concept of spreading model, introduced and studied in the present paper.

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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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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: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph