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2018 | OriginalPaper | Chapter

On Some Properties of A Inherited by C b(X, A)

Authors : Alejandra García, Lourdes Palacios, Carlos Signoret

Published in: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Publisher: Springer International Publishing

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Abstract

Let X be a completely regular Hausdorff space or a pseudocompact Hausdorff space. We denote by C(X, A) the algebra of all continuous functions on X with values in a complex unital locally pseudo-convex algebra A. Let C b(X, A) be its subalgebra consisting of all bounded continuous functions endowed with the topology given by the uniform pseudo-seminorms of A on X. In this paper we examine some properties of A that are inherited by C b(X, A); these properties are projective limit decomposition, inversion, involution, spectral properties and metrizability.

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previous chapter The Metric Structure of Linear Codes
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Footnotes
1
It exists when A is commutative (see [17], p.26).
 
2
The proof of this property involves only real scalars, so there is no problem with the conjugate-homogenity of the involution.
 
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Metadata
Title
On Some Properties of A Inherited by C b(X, A)
Authors
Alejandra García
Lourdes Palacios
Carlos Signoret
Copyright Year
2018
Book
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Print ISBN: 978-3-319-96826-1

Electronic ISBN: 978-3-319-96827-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-96827-8_25

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