Geodesic
On the Boundary and Tensor Product of Function Algebras
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 103-106

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

Let be an arbitrary family of continuous complex-valued functions defined on a compact Hausdorff space X. A closed subset B ⊆ X is called a boundary for if every attains its maximum modulus at some point of B. A boundary, B, is said to be minimal if there exists no boundary for properly contained in B. It can be shown that minimal boundaries exist regardless of the algebraic structure which may possess. Under certain conditions on the family , it can be shown that a unique minimal boundary for exists. In particular, this is the case if is a subalgebra or subspace of C(X) where X is compact and Hausdorff (see for example [2]). This unique minimal boundary for an algebra of functions is called the Silov boundary of . 
On the Boundary and Tensor Product of Function Algebras. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 103-106. doi: 10.4153/CMB-1966-014-5
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[1] 1. Arens, R. and Singer, I. M., Function Values as Boundary Integrals, Proc. Amer. Math. Soc., Vol. 5, 1954, pp. 735-745. Google Scholar

[2] 2. Bear, H. S., The śilov Boundary for a Linear Space of Continuous Functions, Amer. Math. Monthly, May 1961, pp. 483. Google Scholar

[3] 3. Naimark, M.A., Normed Rings, Noordhoff, 1959, pp.212 et seq. Google Scholar

[4] 4. Rickart, C. E., The General Theory of Banach Algebras, Van Nostrand, 1960. Google Scholar

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