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We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological *-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. Let S be a locally compact topological semigroup and M (S) be the Banach algebra of all bounded regular Borel… (More)

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in which we have investigated a similar relation on inverse semigroups. We use a new concept of " restricted "… (More)

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in which we have investigated the concept of " restricted " positive definite functions and their relation with… (More)

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

The Fourier and Fourier-Stieltjes algebras A(G) and B(G) of a locally compact group G are introduced and studied in 60's by Piere Eymard in his PhD thesis. If G is a locally compact abelian group, then A(G) ≃ L 1 (ˆ G), and B(G) ≃ M (ˆ G), via the Fourier and Fourier-Stieltjes transforms, wherê G is the Pontryagin dual of G. Recently these algebras are… (More)

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