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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Notes
- 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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Acknowledgements
We want to thank the referee for his useful suggestions. The first author was partially supported by CONACyT Grant 200917, México.
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García, A., Palacios, L., Signoret, C. (2018). On Some Properties of A Inherited by C b(X, A). In: Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. https://doi.org/10.1007/978-3-319-96827-8_25
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