Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groupoids and Hermitian Banach *-algebras   We study when the twisted groupoid Banach $*$-algebra
$L^1(\mathcal{G},\sigma)$ is Hermitian. In particular, we prove that Hermitian
groupoids satisfy the weak containment property. Furthermore, we find that for
$L^1(\mathcal{G},\sigma)$ to be Hermitian it is sufficient that $L^1
(\mathcal{G}_\sigma)$ is Hermitian. Moreover, if $\mathcal{G}$ is ample, we
find necessary conditions for $L^1(\mathcal{G},\sigma)$ to be Hermitian in
terms of the fibers $\mathcal{G}^x_x$.

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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci