Abstract
In this paper we study some conditions on (not necessarily continuous) linear maps T T between spaces of real- or complex-valued continuous functions C ( X ) C (X) and C ( Y ) C (Y) which allow us to describe them as weighted composition maps. This description depends strongly on the topology in X X ; namely, it can be given when X X is N \mathbb {N} -compact, but cannot in general if some kind of connectedness on X 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 K \mathbb {K} is a field endowed with a nonarchimedean valuation and it is not locally compact.
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