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Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L 1 (G) and the measure algebra M (G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C0(Ω) of the C *-algebra C0(Ω) for a locally compact space Ω, recognizing this space as C(Ω), where Ω is the hyper-Stonean(More)
Let A be a Banach algebra, with second dual space A. We propose to study the space A as a Banach algebra. There are two Banach algebra products on A , denoted by 2 and 3. The Banach algebra A is Arens regular if the two products 2 and 3 coincide on A. In fact, A has two topological centres denoted by Z (1) t (A) and Z (2) t (A) with A ⊂ Z (j) t (A) ⊂ A (j =(More)