Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On function and operator modules   Let $A$ be a unital Banach algebra. We give a characterization of the left
Banach $A$-modules $X$ for which there exists a commutative unital
$C^*$-algebra $C(K)$, a linear isometry $i\colon X\to C(K)$, and a contractive
unital homomorphism $\theta\colon A\to C(K)$ such that $i(a\cdotp x)
=\theta(a)i(x)$ for any $a\in A, x\in X$. We then deduce a "commutative"
version of the Christensen-Effros-Sinclair characterization of operator
bimodules. In the last section of the paper, we prove a $w^*$-version of the
latter characterization, which generalizes some previous work of Effros and
Ruan.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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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: math-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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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: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin