Geodesic
A remark on strict uniform algebras
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2010), pp. 35-39.

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We study some properties of algebras of bounded continuous functions on a completely regular space, these algebras being equipped with the strong topology defined by of family multiplication operators (strict uniform algebras). We prove an analog of a theorem due to M. Sheinberg for strict uniform algebras (see [1–3]).
Keywords: strict uniform algebra
Mots-clés : amenable algebra, bimodule. 
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M. I. Karakhanyan; T. M. Khudoyan. A remark on strict uniform algebras. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2010), pp. 35-39. http://geodesic.mathdoc.fr/item/UZERU_2010_3_a3/

[1] M. V. Sheinberg, “A characterization of the algebra $C(\Omega)$ in terms of cohomology groups”, Uspekhi Mat. Nauk, 32:5(197) (1977), 203–204 (in Russian) | MR | Zbl

[2] Funct. Anal. Appl., 43:1 (2009), 69–71 | DOI | DOI | MR | Zbl

[3] Siberian Math. J., 50:1 (2009), 77–85 | DOI | DOI | MR

[4] I.M. Gelfand, D.A. Raikov, G.E. Shilov, Commutative Normed Rings, Izd. Fiz.-Mat. Lit., M., 1960 (in Russian) | MR

[5] A.V. Arkhangelskii, V.I. Ponomarev Fundamentals of General Topology in Problems and Exercise, Nauka, M., 1974 (in Russian)

[6] R.C. Buck, “Bounded continuous functions on a locally compact space”, Michigan Math. J., 5:2 (1958), 95–104 | DOI | MR | Zbl

[7] F.D. Sentilles, “Bounded continuous functions on a completely regular space”, Trans. Amer. Math. Soc., 168 (1972), 311–336 | DOI | MR | Zbl

[8] R. Giles, “A Generalization of the Strict Topology”, Trans. Amer. Math. Soc., 161 (1971), 467–474 | DOI | MR | Zbl

[9] I. Glicksberg, “Bishop's generalized Stone-Weierstrass theorem for the strict topology”, Proc. Amer. Math. Soc., 14 (1963), 329–333. | MR | Zbl

[10] B.E. Johnson, “Cohomology in Banach algebras”, Memoirs of the American Mathematical Society, 127, American Mathematical Society, Providence, R.I., 1972, 96 pp. | MR | Zbl

[11] M. Reed, B. Simon, Methods of modern mathematical physics, v. 1, Functional Analysis Acad. Press, New York–London, 1972

[12] J.B. Conway, “The strict topology and compactness in the space of measures. II”, Trans. Amer. Math. Soc., 126 (1967), 474–486 | DOI | MR | Zbl