Ievgen Bilokopytov

Date: | Tuesday, September 26, 2017 |
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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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