Continuity and Holomorphicity of Symbols of Weighted Composition Operators

摘要

The main problem considered in this article is the following: if F, E are normed spaces of continuous functions over topological spaces X and Y respectively, and omega : Y -> C and Phi : Y -> X are such that the weighted composition operator W-Phi,W-omega is continuous from F into E, when can we guarantee that both Phi and omega are continuous? An analogous problem is also considered in the context of spaces of holomorphic functions over complex manifolds. Additionally, we consider the most basic properties of the weighted composition operators, which only have been proven before for more concrete function spaces.