Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amenability properties of Rajchman algebras   Rajchman measures of locally compact Abelian groups are studied for almost a
century now, and they play an important role in the study of trigonometric
series. Eymard's influential work allowed generalizing these measures to the
case of \emph{non-Abelian} locally compact groups $G$. The Rajchman algebra of
$G$, which we denote by $B_0(G)$, is the set of all elements of the
Fourier-Stieltjes algebra that vanish at infinity.
  In the present article, we characterize the locally compact groups that have
amenable Rajchman algebras. We show that $B_0(G)$ is amenable if and only if
$G$ is compact and almost Abelian. On the other extreme, we present many
examples of locally compact groups, such as non-compact Abelian groups and
infinite solvable groups, for which $B_0(G)$ fails to even have an approximate
identity.

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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: stat