On algebras of bounded continuous functions valued in a topological algebra

• Autorzy: Arizmendi-Peimbert H. , Chō M. , Garcia A.

Identyfikatory

DOI

10.14708/cm.v57i2.1143

• Języki publikacji: EN

Abstrakty

EN

Let X be a completely regular space. We denote by C(X,A) the locally convex algebra of all continuous functions on X valued in a locally convex algebra A with a unit e. Let C_b(X,A) be its subalgebra consisting of all bounded continuous functions and endowed with the topology given by the uniform seminorms of A on X. It is clear that A can be seen as the subalgebra of the constant functions of C_b(X,A). We prove that if A is a Q-algebra, that is, if the set G(A) of the invertible elements of A is open, or a Q-álgebra with a stronger topology, then the same is true for C_b(X,A).

Słowa kluczowe

EN

m-convex algebras; Q-algebras; advertibly complete algebras; sequentially complete uniformly A-convex algebra; maximal ideal space

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2017
• Tom: Vol 57, No. 2
• Strony: 123--129
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Arizmendi-Peimbert H.

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F. 04510, México

autor

Chō M.

• Department of Mathematics, Faculty of Science, Kanagawa University, Hiratsuka , 259-1293, Japan

autor

Garcia A.

• Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Vicentina, Iztapalapa, 09340 Ciudad de México, D.F., México

Bibliografia

• [1] H. Arizmendi, A. Carrillo, and A. García, On algebras of Banach algebra-valued bounded continuous functions, Rocky Mout. Jour. Math. 46(2016), no. 2, 389-398, DOI 10.1216/RMI-2016-46-2-389.
• [2] H. Arizmendi, A. Carrillo, and R. Pérez, Onmaximal ideals in advertibly complete m-convex algebras, Rend. Circ.Mat. Palermo 60(2011), no. 1-2, 51-57, DOI 10.1007/s12215-011-00.
• [3] H. Arizmendi and P. Ramos, On some properties of uniformly A-convex algebras, manuscript.
• [4] A. Mallios, Topological algebras. Selected Topics, North Holland Mathematics Studies, vol 124, Amsterdam, 1986.
• [5] M. Oudadess, Une norme d’algebre de Banach dans les algebres localement uniformément A-convexes completes, Afrika Math. 9(1987), 15-22.
• [6] H. L. Royden, Function Algebras, Bull. Amer. Math. Soc. 69(1963), 281-298, DOI 10.1090/S0002-9904-1963-10900-1.