Centered weighted composition operators on $L^2$-spaces revisited
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918451502645248 |
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| author | Budzyński, Piotr |
| author_facet | Budzyński, Piotr |
| contents | Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally half-centered operators is introduced, and it is shown that unbounded weighted composition operators are spectrally half-centered provided their powers are closed and densely defined. A criteria for centered weighted shifts on directed trees of types I--IV are provided. Various examples are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Centered weighted composition operators on $L^2$-spaces revisited Budzyński, Piotr Functional Analysis 47B37 (Primary) 47A15, 47B20, 47B33 (Secondary) Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally half-centered operators is introduced, and it is shown that unbounded weighted composition operators are spectrally half-centered provided their powers are closed and densely defined. A criteria for centered weighted shifts on directed trees of types I--IV are provided. Various examples are presented. |
| title | Centered weighted composition operators on $L^2$-spaces revisited |
| topic | Functional Analysis 47B37 (Primary) 47A15, 47B20, 47B33 (Secondary) |
| url | https://arxiv.org/abs/2603.03594 |