Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity and amenability of weighted Banach algebras and their second
  dual on locally compact groups   Let $\omega $ be a weight function on a locally compact group G mand let $
M_* (G, \omega ) $ be the subspace of $ M(G , \omega )^* $ consisting of all
functionals that vanish at infinity. In this paper, we first investigate the
Arens regularity of $ M_* (G, \omega )^* $ and show that $ M_* (G, \omega )^* $
is Arnes regular if and only if G is finite or $ \omega $ is zero cluster. This
result is an answer to the question posed and it improves some well-known
results. We also give necessary and sufficient criteria for the weight function
spaces $ Wap(G , 1/ \omega ) $ and $ Wap(G , 1/ \omega ) $ to be equal to $ C_b
(G , 1/ \omega ) $. We prove that for non-compact group G, the Banach algebra $
M_* (G, \omega )^* $ is Arnes regular if and only if $ Wap(G , 1/ \omega ) =
C_b (G , 1/ \omega ) $. We then investigate amenability of $ M_* (G, \omega )^*
$ and prove that $ M_* (G, \omega )^* $ is amenable and Arnes regular if and
only if G is finite.

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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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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: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: physics