Ievgen Bilokopytov

## Continuity and Holomorphicity of Symbols of Weighted Composition Operators

Date: Tuesday, September 26, 2017

We consider the following problem: if $$\mathbf{F}$$ and $$\mathbf{E}$$ are (general) normed spaces of continuous functions over topological spaces $$X$$ and $$Y$$ respectively, and $$\omega:Y\to\mathbb{C}$$ and $$\Phi:Y\to X$$ are such that the weighted composition operator $$W_{\Phi,\omega}$$ is continuous, when can we guarantee that both \$$$\Phi$$ and $$\omega$$ are continuous? An analogous problem is also considered in the context of normed spaces of holomorphic functions.

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