Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measures of noncompactness on the standard Hilbert $C^*$-module   We define a measure of noncompactness $\lambda$ on the standard Hilbert
$C^*$-module $l^2(\mathcal A)$ over a unital $C^*$-algebra, such that
$\lambda(E)=0$ if and only if $E$ is $\mathcal A$-precompact (i.e.\ it is
$\varepsilon$-close to a finitely generated projective submodule for any
$\varepsilon>0$) and derive its properties. Further, we consider the known,
Kuratowski, Hausdorff and Istr\u{a}\c{t}escu measure of noncomapctnes on
$l^2(\mathcal A)$ regarded as a locally convex space with respect to a suitable
topology, and obtain their properties as well as some relationship between them
and introduced measure of noncompactness $\lambda$.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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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: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th