The Measure Algebra as an Operator Algebra
نویسنده
چکیده
Introduction. In § I, it is shown that M(G)*, the space of bounded linear functionals on M(G), can be represented as a semigroup of bounded operators on M(G). Let A denote the non-zero multiplicative linear functionals on M(G) and let P be the norm closed linear span of A in M(G)*. In § II, it is shown that P , with the Arens multiplication, is a commutative J3*-algebra with identity. Thus P = C(B), where B is a compact, Hausdorff space. In § III, it is shown that B, with a natural multiplication, is a compact Abelian semigroup and that M(G) is topologically embedded in M(B). This gives a simplified construction of the Taylor structure semigroup for M(G).
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