Geodesic
On algebras of bounded continuous functions valued in a topological algebra
Commentationes Mathematicae, Tome 57 (2017) no. 2, pp. 123-129.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let \(X\) be a completely regular space. We denote by \(C\left(X,A\right) \) the locally convex algebra of all continuous functions on \(X\) valued in a locally convex algebra \(A\) with a unit \(e.\) Let \(C_{b}\left(X,A\right) \) 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 \(C_{b}\left(X,A\right)\). We prove that if \(A\) is a Q-algebra, that is, if the set \(G\left( A\right) \) of the invertible elements of \(A\) is open, or a Q-\'{a}lgebra with a stronger topology, then the same is true for \(C_{b}\left( X,A\right) \).
DOI : 10.14708/cm.v57i2.1143
Classification : 46J10, 46E40, 46H05
Mots-clés : m-convex algebras, Q-algebras, advertibly complete algebras, sequentially complete uniformly A-convex algebra, maximal ideal space 
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Hugo Arizmendi Peimbert; Muneo Cho; Alejandra García García. On algebras of bounded continuous functions valued in a topological algebra. Commentationes Mathematicae, Tome 57 (2017) no. 2, pp.  123-129. doi : 10.14708/cm.v57i2.1143. http://geodesic.mathdoc.fr/articles/10.14708/cm.v57i2.1143/

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