Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amenable semigroups and nonexpansive dynamical systems   We characterize amenability of subspaces of $C(S)$, where $S$ is a
semitopological semigroup, in terms of fixed point properties of nonexpansive
actions. In particular, we give a complete characterization of a
semitopological semigroup with a left invariant mean on WAP(S) that answers a
question of A.T.-M. Lau and Y. Zhang in the affirmative. We also propose a new
approach to Lau's problem concerning a counterpart of Day-Mitchell's
characterization of amenable semigroups and show some partial results, in the
case of weak$^{\ast }$ compact convex sets with the Radon-Nikod\'{y}m property,
and in the duals of $M$-embedded Banach spaces.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int