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Abstract. We characterize the mappings inducing the weighted composition operators on $LV_b(X)$ and $LV_0(X)$, the weighted locally convex spaces of cross-sections with the topology generated by seminorms which are weighted analogoues of the supremum norm. A few properties of the composition operators are discussed and some examples of weighted composition operators are presented to illustrate the theory. The paper presents a broad account of the theory of these operators on weighted spaces of functions. Some of the results of [7], [10] and [11] can be derived as an application of the results presented in this paper.
AMS Subject Classification
(1991): 47B38, 46E40
Keyword(s):
Weighted composition operators,
weighted spaces of cross-sections,
seminorms
Received March 8, 1994. (Registered under 5598/2009.)
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