CHANGES IN "CROWNS" IN TOPOLOGICAL ALGEBRAS OF FUNCTIONS

Tigran M. Khudoyan; Martin I. Karakhanyan

doi:10.46991/PYSUA.2024.58.3.073

Authors

Tigran M. Khudoyan National Polytechnic University of Armenia (NPUA), Armenia https://orcid.org/0009-0004-4115-2454
Martin I. Karakhanyan National Polytechnic University of Armenia (NPUA), Armenia

DOI:

https://doi.org/10.46991/PYSUA.2024.58.3.073

Keywords:

topological "crown", algebra, space of maximal ideals, continuous functions, linear multiplicative functionals

Abstract

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.

References

Carleson L. On Bounded Analytic Functions and Closure Problems. Ark. Mat. 2 (1952), 283-291. https://doi.org/10.1007/BF02590884

Gofman K. Banach Spaces of Analytic Functions. Moscow, Foreign Literature (1963).

Grigorian S., Karakhanyan M., Khor'kova T. About Beta-uniform Dirichlet Algebras. Izv. Akad. Nauk Armenii. Math. 45 (2010), 17-26 (in Russian). https://doi.org/10.3103/S1068362310060026

Gelfand I.M., Raikov D.A., Shilov G.E. Commutative Normalized Rings. Moscow, FIZMATLIT (1960), 315 (in Russian).

Gamelin T. Uniform Algebras. Moscow, Mir (1973), 336 (in Russian).

Karakhanyan M.I., Khor'kova T.A. A Characterization of the Algebra Cβ(Ω). Functional Anal. and Its Applic. 13 (2009), 69-71. https://doi.org/10.1007/s10688-009-0008-z

Buck R.C., Wells J. Bounded Continuous Functions on a Locally Compact Space. Michigan Mathematical Journal 5 (1958), 95-104. https://doi.org/10.1307/MMJ/1028998054

Canway J.B. The Strict Topology and Compactness in the Space of Measures. II. Trans. Amer. Math. Soc. 126 (1967), 474-486. https://doi.org/10.2307/1994310

Giles R. A Generalization of the Strict Topology. Trans. Amer. Math. Soc. 161 (1971), 467-474. https://doi.org/10.2307/1995954

Schaefer H. H. Topological Vector Spaces. New York, The Macmillan Co. (1966), 360. https://doi.org/10.1007/978-1-4612-1468-7

Karakhanyan M.I., Khudoyan T.M. A Remark on Strict Uniform Algebras. Proc. of the YSU. Phys. and Math. Sci. 3 (2010), 35-39. https://doi.org/10.46991/PYSUA.2010.44.3.035