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- W2024395775 abstract "Let G be a topological semigroup, i.e. G is a semigroup with a Hausdorff topology such that the map ( a , b ) → a.b from G × G into G is continuous when G × G has the product topology. Let C(G ) denote the space of complex-valued bounded continuous functions on G with the supremum norm. Let LUC ( G ) denote the space of bounded left uniformly continuous complex-valued functions on G i.e. all f ε C(G ) such that the map a → l a f of G into C(G ) is continuous when C(G ) has a norm topology, where ( l a f )( x ) = f (ax) (a, x ε G ). Then LUC ( G ) is a closed subalgebra of C(G ) invariant under translations. Furthermore, if m ε LUC ( G )*, f ε LUC ( G ), then the function is also in LUC ( G ). Hence we may define a product for n, m ε LUC( G )*. LUC ( G )* with this product is a Banach algebra. Furthermore, ʘ is precisely the restriction of the Arens product defined on the second conjugate algebra l ∞ ( G )* = l 1 ( G )** to LUC ( G )*. We refer the reader to [ 1 ] and [ 10 ] for more details." @default.
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- W2024395775 date "1986-03-01" @default.
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- W2024395775 title "Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups" @default.
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- W2024395775 doi "https://doi.org/10.1017/s0305004100064197" @default.
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