Difference of weighted composition operators between Bergman spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916864961019904 |
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| author | Du, Jiaoye Tong, Cezhong Yang, Zicong |
| author_facet | Du, Jiaoye Tong, Cezhong Yang, Zicong |
| contents | We first obtain a simpler proof of the main results in [IEOT, {\bf 93}(2021), 17], which characterized the bounded and compact differences $C_{u,φ}-C_{v,ψ}$ of two weighted composition operators acting from $A_α^p(\mathbb{D})$ to $A_α^q(\mathbb{D})$. Then we get some characterizations for the difference of weighted composition operator belonging to Schatten class. Moreover, compact difference of a weighted composition operator and a unweighted composition operator on Hardy space is also studied. It shows a rigidity, i.e. $C_{u,φ}-C_ψ$ is compact on $H^{2}(\mathbb{D})$ if and only if both $C_{u',φ}:H^2(\mathbb{D})\to A_{1}^2(\mathbb{D})$ and $C_{uφ',φ}-C_{ψ',ψ}:A_{1}^2(\mathbb{D})\to A_{1}^2(\mathbb{D})$ are compact, which generalize a result in [JFA, {\bf 278}(2020), 108401]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Difference of weighted composition operators between Bergman spaces Du, Jiaoye Tong, Cezhong Yang, Zicong Functional Analysis Complex Variables 30H20, 47B33 We first obtain a simpler proof of the main results in [IEOT, {\bf 93}(2021), 17], which characterized the bounded and compact differences $C_{u,φ}-C_{v,ψ}$ of two weighted composition operators acting from $A_α^p(\mathbb{D})$ to $A_α^q(\mathbb{D})$. Then we get some characterizations for the difference of weighted composition operator belonging to Schatten class. Moreover, compact difference of a weighted composition operator and a unweighted composition operator on Hardy space is also studied. It shows a rigidity, i.e. $C_{u,φ}-C_ψ$ is compact on $H^{2}(\mathbb{D})$ if and only if both $C_{u',φ}:H^2(\mathbb{D})\to A_{1}^2(\mathbb{D})$ and $C_{uφ',φ}-C_{ψ',ψ}:A_{1}^2(\mathbb{D})\to A_{1}^2(\mathbb{D})$ are compact, which generalize a result in [JFA, {\bf 278}(2020), 108401]. |
| title | Difference of weighted composition operators between Bergman spaces |
| topic | Functional Analysis Complex Variables 30H20, 47B33 |
| url | https://arxiv.org/abs/2507.19735 |