Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Gromov-Hausdorff convergence for operator metric spaces   We introduce an analogue for Lip-normed operator systems of the second
author's order-unit quantum Gromov-Hausdorff distance and prove that it is
equal to the first author's complete distance. This enables us to consolidate
the basic theory of what might be called operator Gromov-Hausdorff convergence.
In particular we establish a completeness theorem and deduce continuity in
quantum tori, Berezin-Toeplitz quantizations, and theta-deformations from work
of the second author. We show that approximability by Lip-normed matrix
algebras is equivalent to 1-exactness of the underlying operator space and, by
applying a result of Junge and Pisier, that for n greater than or equal to 7
the set of isometry classes of n-dimensional Lip-normed operator systems is
nonseparable. We also treat the question of generic complete order structure.

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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph