Accession Number : AD0651890

Title :   THE MEASURE ALGEBRA AS AN OPERATOR ALGEBRA.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE

Personal Author(s) : Rameriz,Donald E.

Report Date : 1967

Pagination or Media Count : 19

Abstract : Let G be a locally compact abelian group; M(G) the algebra of bounded, Borel measures on G; and M(G)' the algebra of Fourier-Stieltjes transforms. In Chapter I, we show how the bounded linear functionals on M(G) can be represented as the semigroup of bounded operators on M(G)' which commute with translation. We say that M(G)' is an operator algebra. Let M(G)* denote the topological dual of M(G); M sub M(G) the multiplicative linear functionals on M(G); and P the closed linear span of M sub M(G) in M(G)*, P = M sub M(G) tc M(G)*. Since M(G)' is an operator algebra, we may induce in P a natural multiplication. In Chapter II, it is shown that P is a commutative B* - algebra with 1. Thus P = C(B), where B is a compact, Hausdorff space. In Chapter III, we show that B is a compact abelian semi-group and that M(G) is topologically embedded in M(B). B is the Taylor structure semi-group for M(G). This gives a simplified construction of the Taylor structure semi-group for M(G). (Author)

Descriptors :   (*GROUPS(MATHEMATICS), THEORY), FOURIER ANALYSIS, OPERATORS(MATHEMATICS), MATHEMATICS, ALGEBRAS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE