On algebras of bounded continuous functions valued in a topological algebra

Hugo Arizmendi Peimbert, Muneo Cho, and Alejandra García García. "On algebras of bounded continuous functions valued in a topological algebra." Commentationes Mathematicae 57.2 (2017): null. <http://eudml.org/doc/292470>.

@article{HugoArizmendiPeimbert2017,
abstract = {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-álgebra with a stronger topology, then the same is true for $C_\{b\}\left( X,A\right) $.},
author = {Hugo Arizmendi Peimbert, Muneo Cho, Alejandra García García},
journal = {Commentationes Mathematicae},
keywords = {m-convex algebras; Q-algebras; advertibly complete algebras; sequentially complete uniformly A-convex algebra; maximal ideal space},
language = {eng},
number = {2},
pages = {null},
title = {On algebras of bounded continuous functions valued in a topological algebra},
url = {http://eudml.org/doc/292470},
volume = {57},
year = {2017},
}

TY - JOUR
AU - Hugo Arizmendi Peimbert
AU - Muneo Cho
AU - Alejandra García García
TI - On algebras of bounded continuous functions valued in a topological algebra
JO - Commentationes Mathematicae
PY - 2017
VL - 57
IS - 2
SP - null
AB - 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-álgebra with a stronger topology, then the same is true for $C_{b}\left( X,A\right) $.
LA - eng
KW - m-convex algebras; Q-algebras; advertibly complete algebras; sequentially complete uniformly A-convex algebra; maximal ideal space
UR - http://eudml.org/doc/292470
ER -