Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amenable groups and a geometric view on unitarisability   We investigate unitarisability of groups by looking at actions on the cone of
positive invertible operators of a Hilbert space. This way, we give a geometric
prove to a result by Gilles Pisier on the existence of some universal constants
for unitarisable groups. By constructing barycenters for finite sets in a some
class of geodesic metric spaces, we prove a fixed point theorem for actions of
amenable groups by isometries. In particular, we show that extensions of
unitarisable groups by amenable groups are unitarisable and virtual
unitarisability implies unitarisability and estimate the corresponding
universal constants.

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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: astro-ph