In this paper we initiate the study of real group algebras and investigate some of its aspects. Let L1 (G) be a group algebra of a locally compact group G,τ :G →G be a group homeomorphism such that τ 2 =τοτ = 1, the identity map, and Lp (G,τ ) = { f ∈ Lp (G) : fοτ = f } ( p ≥ 1) . In this paper, among other results, we clarify the structure of Lp (G,τ ) and characterize amenability of L1 (G,τ ) and identify its multipliers.
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