On Lebesgue-type decompositions for Banach algebras

On Lebesgue-type decompositions for Banach algebras

If the maximal ideal space of a commutative complex unitary Banach algebra, X, is equipped with a nonnegative, finite, regular Borel measure, m, then for each element, x, in X, a. complex regular Borel measure, mx, can be obtained by integrating the Gelfand transform of x with respect to m over the...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 1970-08, Vol.3 (1), p.39-47
1. Verfasser: Anton, Howard
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description If the maximal ideal space of a commutative complex unitary Banach algebra, X, is equipped with a nonnegative, finite, regular Borel measure, m, then for each element, x, in X, a. complex regular Borel measure, mx, can be obtained by integrating the Gelfand transform of x with respect to m over the Borel sets. This paper considers the possibility of direct sum decompositions of the form X = Ax ⊕ Px where Ax = {z ε X: mz ≪ mx} and Px = {z ε X: mz ┴ mx}.
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title On Lebesgue-type decompositions for Banach algebras
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