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The Measure Algebra as an Operator Algebra

Published online by Cambridge University Press:  20 November 2018

Donald E. Ramirez
Donald E. Ramirez*
Affiliation:
University of Virginia, Charlottesville, Virginia
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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 △ denote the non-zero multiplicative linear functionals on M(G) and let P be the norm closed linear span of △ in M(G)*. In § II, it is shown that P, with the Arens multiplication, is a commutative B*-algebra with identity. Thus P = C(B), where B is a compact, Hausdorff space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1391 - 1396
Copyright
Copyright © Canadian Mathematical Society 1968

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