Geodesic
Functionals on Real C(S)
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 490-498

Voir la notice de l'article provenant de la source Cambridge University Press

The maximal ideals in a commutative Banach algebra with identity have been elegantly characterized [5; 6] as those subspaces of codimension one which do not contain invertible elements. Also, see [1]. For a function algebra A, a closed separating subalgebra with constants of the algebra of complex-valued continuous functions on the spectrum of A, a compact Hausdorff space, this characterization can be restated: Let F be a linear functional on A with the property:(*) For each ƒ in A there is a point s, which may depend on f, for which F(f) = f(s). 
Farnum, Nicholas; Whitley, Robert. Functionals on Real C(S). Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 490-498. doi: 10.4153/CJM-1978-044-8
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[1] 1. Browder, A., Introduction to function algebras (Benjamin, 1969). Google Scholar

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[5] 5. Gleason, A., A characterization 0﹜ maximal ideals, J. D'Analyse Math. V.) (1967), 171–172. Google Scholar

[6] 6. Kahane, J. P. and Zelazko, W., A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 340–343. Google Scholar

[7] 7. Taylor, A., Introduction to Junctional analysis (Wiley, 1958). Google Scholar

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