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"A Representation Theorem for Positive Functionals on Involution Algebras" .
"representation theorem" .
"R. S." .
"1966-01-01" .
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_:Ne4dd4946757844a6b7f6475b614caeff .
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_:N948314fb96574fe38a4e1d22eeeb3fd6 "Springer Nature - SN SciGraph project" .
"positive multiplicative linear functionals" .
"G." .
"D. Raikov has shown [6] that for a commutative Banach algebra A with symmetric involution, the set p of positive linear functionals on A having norm at most one is isometrically isomorphic to the set of positive measures (of norm at most one) defined on the maximal ideal space of A. Raikov\u2019s proof of this theorem depends on the Gelfand theory of commutative Banach algebras and the Riesz-Markov Theorem (see also [8; p. 230]). Here we shall give a new and elementary proof of Raikov\u2019s result by first proving a Radon-Nikodym type theorem for positive functionals (Theorem 1) and then showing directly that the extreme points of the compact convex set of positive linear functionals in the unit ball of A\u2032 are exactly the set M of positive multiplicative linear functionals (Theorem 2). An application of the Krein-Milman Theorem makes possible the representation of every element of p as the centroid of a positive measure on M (Theorem 3) and uniqueness of this representation is a consequence of the Stone-Weierstrass Theorem." .
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_:N948314fb96574fe38a4e1d22eeeb3fd6 .
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_:N84c4c8a7fadb4e03b3e3bfb475e8d0fe "Contributions to Functional Analysis" .
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_:N681c7afbcabb4c61936fbc0a7bc6bdc5 .
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"2022-01-01T19:28" .
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_:N84c4c8a7fadb4e03b3e3bfb475e8d0fe "978-3-642-85999-1" .
"Involution Algebras" .
"compact convex sets" .
"https://scigraph.springernature.com/explorer/license/" .
_:Na4cddb1995cd416db9c0e1de29452127 "Springer Nature" .
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