COMPACT AND HILBERT–SCHMIDT WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES
| Autor: | CHING-ON LO, ANTHONY WAI-KEUNG LOH |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of the Australian Mathematical Society. 113:208-225 |
| ISSN: | 1446-8107 1446-7887 |
| DOI: | 10.1017/s1446788722000039 |
| Popis: | Let u and $\varphi $ be two analytic functions on the unit disk D such that $\varphi (D) \subset D$ . A weighted composition operator $uC_{\varphi }$ induced by u and $\varphi $ is defined on $A^2_{\alpha }$ , the weighted Bergman space of D, by $uC_{\varphi }f := u \cdot f \circ \varphi $ for every $f \in A^2_{\alpha }$ . We obtain sufficient conditions for the compactness of $uC_{\varphi }$ in terms of function-theoretic properties of u and $\varphi $ . We also characterize when $uC_{\varphi }$ on $A^2_{\alpha }$ is Hilbert–Schmidt. In particular, the characterization is independent of $\alpha $ when $\varphi $ is an automorphism of D. Furthermore, we investigate the Hilbert–Schmidt difference of two weighted composition operators on $A^2_{\alpha }$ . |
| Databáze: | OpenAIRE |
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