Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator Figa-Talamanca-Herz algebras   Let G be a locally compact group. We use the canonical operator space
structure on the spaces $L^p(G)$ for $p \in [1,\infty]$ introduced by G. Pisier
to define operator space analogues $OA_p(G)$ of the classical
Figa-Talamanca-Herz algebras $A_p(G)$. If $p \in (1,\infty)$ is arbitrary, then
$A_p(G) \subset OA_p(G)$ such that the inclusion is a contraction; if p = 2,
then $OA_2(G) \cong A(G)$ as Banachspaces spaces, but not necessarily as
operator spaces. We show that $OA_p(G)$ is a completely contractive Banach
algebra for each $p \in (1,\infty)$, and that $OA_q(G) \subset OA_p(G)$
completely contractively for amenable $G$ if $1 < p \leq q \leq 2$ or $2 \leq q
\leq p < \infty$. Finally, we characterize the amenability of G through the
existence of a bounded approximate identity in $OA_p(G)$ for one (or
equivalently for all) $p \in (1,\infty)$.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci