Strong Arens irregularity of Beurling algebras with a locally convex topology |
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Authors: | S Maghsoudi R Nasr-Isfahani A Rejali |
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Institution: | (1) Department of Mathematics, University of Isfahan, Isfahan, Iran;(2) Department of Mathematics, Isfahan University of Technology, Isfahan, Iran |
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Abstract: | Let G be a locally compact group with a weight function ω. Recently, we have shown that the Banach space L0∞ (G,1/ω) can be identified with the strong dual of L1(G, ω)equipped with some locally convex topologies τ. Here we use this duality to introduce an Arens multiplication on (L1(G, ω), τ)**, and prove that the topological center of (L1(G, ω), τ)** is (L1(G, ω); this enables us to conclude that (L1(G, ω), τ) is Arens regular if and only if G is discrete. We also give a characterization for Arens regularity of L0∞ (G, 1/ω)1.
Received: 8 March 2005 |
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Keywords: | , |
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