On algebras of bounded continuous functions valued in a topological algebra

• Autorzy: Hugo Arizmendi Peimbert , Muneo Cho , Alejandra García García
• Języki publikacji: EN

Abstrakty

EN

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 \(C_{b}\left( X,A\right) \).

Słowa kluczowe

EN

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

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2017
• Tom: 57
• Numer: 2

Daty

wydano

2017

online

2018-03-20

Twórcy

autor

Hugo Arizmendi Peimbert

autor

Muneo Cho

autor

Alejandra García García

Identyfikatory

DOI

10.14708/cm.v57i2.1143