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$\mathbb{N}$-compactness and weighted composition maps


Author: Jesús Araujo
Journal: Proc. Amer. Math. Soc. 130 (2002), 1225-1234
MSC (2000): Primary 54C35; Secondary 47B38, 46S10, 46E15
DOI: https://doi.org/10.1090/S0002-9939-01-06135-4
Published electronically: September 14, 2001
MathSciNet review: 1873801
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Abstract:

In this paper we study some conditions on (not necessarily continuous) linear maps $T$ between spaces of real- or complex-valued continuous functions $C (X)$ and $C (Y)$ which allow us to describe them as weighted composition maps. This description depends strongly on the topology in $X$; namely, it can be given when $X$ is $\mathbb{N}$-compact, but cannot in general if some kind of connectedness on $X$ is assumed. Finally we also give an infimum-preserving version of the Banach-Stone theorem. The results are also proved for spaces of bounded continuous functions when $\mathbb{K}$ is a field endowed with a nonarchimedean valuation and it is not locally compact.


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Additional Information

Jesús Araujo
Affiliation: Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s. n., E-39071 Santander, Spain
Email: araujo@matesco.unican.es

DOI: https://doi.org/10.1090/S0002-9939-01-06135-4
Received by editor(s): February 2, 2000
Received by editor(s) in revised form: October 19, 2000
Published electronically: September 14, 2001
Additional Notes: This research was supported in part by the Spanish Dirección General de Investigación Científica y Técnica (DGICYT, PB98-1102).
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society

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