Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-asymptotic $\ell_1$ spaces with unique $\ell_1$ asymptotic model   A recent result of Freeman, Odell, Sari, and Zheng states that whenever a
separable Banach space not containing $\ell_1$ has the property that all
asymptotic models generated by weakly null sequences are equivalent to the unit
vector basis of $c_0$ then the space is Asymptotic $c_0$. We show that if we
replace $c_0$ with $\ell_1$ then this result is no longer true. Moreover, a
stronger result of B. Maurey - H. P. Rosenthal type is presented, namely, there
exists a reflexive Banach space with an unconditional basis admitting $\ell_1$
as a unique asymptotic model whereas any subsequence of the basis generates a
non-Asymptotic $\ell_1$ subspace.

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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom