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  • 1 University of Isfahan Department of Mathematics Isfahan Iran
  • 2 Isfahan University of Technology Department of Mathematical Science Isfahan 84156-83111 Iran
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Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted Lp-space Lp(G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for Lp(G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and Lp(G, ω) is a Banach algebra, then G is σ-compact.