ℕ-compactness and weighted composition maps

Araujo, Jesús

doi:10.1090/S0002-9939-01-06135-4

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

Proc. Amer. Math. Soc. 130 (2002), 1225-1234

DOI: https://doi.org/10.1090/S0002-9939-01-06135-4

Published electronically: September 14, 2001

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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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