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- W2052164197 abstract "In this paper we prove that the states of a unital Banach algebra generate the dual Banach space as a linear space (Theorem 2). This is a result of R. T. Moore ( 4 , Theorem 1( a )) who uses a decomposition of measures in his proof. In the proof given here the measure theory is replaced by a Hahn-Banach separation argument. We shall let A denote a unital Banach algebra over the complex field, and D (1) denote { f ∈ A ′: ‖ f ‖ = f (1) = 1} where A ′ is the dual of A . The motivation of Moore's results is the theorem that in a C *-algebra every continuous linear functional is a linear combination of four states (the states are the elements of D (1)) (see ( 2 , 2.6.4, 2.1.9, 1.1.10))." @default.
- W2052164197 created "2016-06-24" @default.
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- W2052164197 date "1971-12-01" @default.
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- W2052164197 title "The states of a Banach algebra generate the dual" @default.
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- W2052164197 doi "https://doi.org/10.1017/s0013091500009627" @default.
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