Geodesic
Choquet Boundary for Real Function Algebras
Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1084-1104

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

The concepts of Choquet boundary and Shilov boundary are well-established in the context of a complex function algebra (see [2] for example). There have been a few attempts to develop the concept of a Shilov boundary for real algebras, [4], [6] and [7]. But there seems to be none to develop the concept of Choquet boundary for real algebras.The aim of this paper is to develop the theory of Choquet boundary of a real function algebra (see Definition (1.8)) along the lines of the corresponding theory for a complex function algebra.In the first section we define a real-part representing measure for a continuous linear functional φ on a real function algebra A with the property ║φ║ = 1 = φ(1). The elements of A are functions on a compact, Hausdorff space X. The Choquet boundary is then defined as the set of those points x ∊ X such that the real part of the evaluation functional, Re(ex ), has a unique real part representing measure. 
Kulkarni, S. H.; Arundhathi, S. Choquet Boundary for Real Function Algebras. Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1084-1104. doi: 10.4153/CJM-1988-045-x
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[1] 1. Bonsall, F. F. and Duncan, J., Complete normed algebras (Springer-Verlag, 1973). Google Scholar | DOI

[2] 2. Browder, A., Introduction to function algebras (W. A. Benjamin Inc., New York, 1969). Google Scholar

[3] 3. Ingelstam, L., Real Banach algebras, Ark. Mat. 5 (1965), 239–270. Google Scholar

[4] 4. Ingelstam, L., Symmetry in real Banach algebras, Math. Scand. 18 (1968), 53–68. Google Scholar

[5] 5. Kulkarni, S. H. and Limaye, B. V., Gleason parts of real function algebras, Can. J. Math. 33 (1981), 181–200. Google Scholar

[6] 6. Limaye, B. V., Boundaries for real Banach algebras, Can. J. Math. 28 (1976), 42–49. Google Scholar

[7] 7. Limaye, B. V. and Simha, R. R., Deficiencies of certain real uniform algebras, Can. J. Math. 27 (1975), 121–132. Google Scholar

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