Geodesic
Changes in “crowns” in topological algebras of functions
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 3, pp. 73-78
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work, for topological algebras of continuous complex-valued functions defined on a locally compact, the change in the topological “crown” of such algebra is studied depending on the topology introduced in it. Note that the concept of the “crown” was previously studied in works [1–3]. However, the concept of the topological “crown” for topological algebras of functions is introduced for the first time in work [3]. In fact, the topological “crown” is the set of all those linear multiplicative functionals that are not continuous on the given topological algebra.
Keywords: topological “crown”, algebra, space of maximal ideals, continuous functions, linear multiplicative functionals 
@article{UZERU_2024_58_3_a0,
     author = {T. M. Khudoyan and M. I. Karakhanyan},
     title = {Changes in {\textquotedblleft}crowns{\textquotedblright} in topological algebras of functions},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {73--78},
     year = {2024},
     volume = {58},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2024_58_3_a0/}
}
TY  - JOUR
AU  - T. M. Khudoyan
AU  - M. I. Karakhanyan
TI  - Changes in “crowns” in topological algebras of functions
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2024
SP  - 73
EP  - 78
VL  - 58
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZERU_2024_58_3_a0/
LA  - en
ID  - UZERU_2024_58_3_a0
ER  - 
%0 Journal Article
%A T. M. Khudoyan
%A M. I. Karakhanyan
%T Changes in “crowns” in topological algebras of functions
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2024
%P 73-78
%V 58
%N 3
%U http://geodesic.mathdoc.fr/item/UZERU_2024_58_3_a0/
%G en
%F UZERU_2024_58_3_a0
T. M. Khudoyan; M. I. Karakhanyan. Changes in “crowns” in topological algebras of functions. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 3, pp. 73-78. http://geodesic.mathdoc.fr/item/UZERU_2024_58_3_a0/

[1] L. Carleson, “On Bounded Analytic Functions and Closure Problems”, Ark. for Mat., 2:2-3 (1952), 283–291 | DOI | MR | Zbl

[2] K. Gofman, Banach Spaces of Analytic Functions, Inostr. Liter., M., 1963 (in Russian) | MR

[3] S. A. Grigoryan, M. I. Karakhanyan, T. A. Khor’kova, “On $\beta$-Uniform Dirichlet Algebras”, Izv. Nat. Acad. Nauk Armenii. Matem., 45:6 (2010), 17–26 (in Russian) | DOI | MR

[4] I. M. Gelfand, D. A. Raikov, G. E. Shilov, Commutative Normalized Rings, PhysMathGhis, Moscow, 1960 (in Russian) | MR

[5] T. Gamelin, The Uniform Algebras, Mir, M., 1975 (in Russian) | MR

[6] M. I. Karakhanyan, T. A. Khor’kova, “A Characterization of the Algebra $C_{\beta} (\Omega)$”, Functional Anal. and its Applic., 13:1 (2009), 69–71 | DOI | MR | Zbl

[7] R. C. Buck, J. Wells, “Bounded Continuous Functions on a Locally Compact Space”, Michigan Math. J., 5:2 (1958), 95–104 | DOI | MR | Zbl

[8] J. B. Canway, “The Strict Topology and Compactness in the Space of Measures. II”, Trans. Amer. Math. Soc., 126 (1967), 474–486 | DOI | MR

[9] R. Giles, Trans. Amer. Math. Soc., 161, 1971, 467–474 | DOI | MR | Zbl

[10] H. H. Schaefer, Topological Vector Spaces, The Macmillan Co., New York, 1966 | DOI | MR | Zbl

[11] M. I. Karakhanyan, T. M. Khudoyan, “A Remark on Strict Uniform Algebras”, Proceedings of the YSU A: Physical and Mathematical Sciences, 2010, no. 3, 35–39 | DOI | Zbl