Geodesic
A function algebra of the second degree on non-localness
Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 253-266 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $A$ be a function algebra with uniform convergence containing the constants, and let $\mathfrak M_A$ be its maximal ideal space. A continuous function $f$ on $\mathfrak M_A$ is called $f$-local if it coincides, in a neighborhood of each point $m\in\mathfrak M_A$, with some function from the algebra $A$. The algebra $A$ is called local if it contains all $A$-local functions, and nonlocal otherwise. A well-known example of a nonlocal algebra has been constructed by E. Kallin. She also raised the question: is there a smallest local closed subalgebra in $C(\mathfrak M_A)$ containing all the $A$-local functions? In this work we give a negative answer to this question. The appropriate algebra is realized as a subalgebra in $C(S)$, where $S$ is a compactum in $C^5$, and is generated by acertain family of rational functions. Bibliography: 5 titles. 
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     title = {A~function algebra of the second degree on non-localness},
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A. D. Varshavskii. A function algebra of the second degree on non-localness. Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 253-266. http://geodesic.mathdoc.fr/item/SM_1969_9_2_a8/

[1] E. Kallin, “A nonlocal function algebra”, Trans. Amer. Math. Soc., 104:1 (1963), 24–36 | MR

[2] G. Stolzenberg, “The maximal ideal space of the functions locally in a function algebra”, Proc. Amer. Math. Soc., 14 (1963), 342–345 | DOI | MR | Zbl

[3] C. E. Rickart, “The maximal ideal space of functions locally approximable in a function algebra”, Proc. Amer. Math. Soc., 17 (1966), 1320–1326 | DOI | MR | Zbl

[4] C. E. Rickart, “Holomorphic convexity for general function algebras”, Canad. J. Math., 20 (1968), 272–290 | MR | Zbl

[5] A. D. Varshavskii, “Funktsionalnaya algebra vtoroi stepeni nelokalnosti”, Uspekhi matem. nauk, XXIV:2(146) (1969), 223–224