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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2604.22284 |
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| _version_ | 1866918469140742144 |
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| author | Zhang, Peiran Tian, Roumei Lu, Yufeng Yang, Yixin Zu, Chao |
| author_facet | Zhang, Peiran Tian, Roumei Lu, Yufeng Yang, Yixin Zu, Chao |
| contents | In this paper, we study the compactness of the product and the commutator of two inner projections on the Hardy spaces over the unit disk and the polydisc. For the single-variable case, we provide a complete characterization of the compactness of the commutator of two inner projections by means of Douglas algebra. In the multivariable setting, we discover a rigidity phenomenon: on the bidisc, the product of two inner projections is compact if and only if it has finite rank, whereas on the polydisc of dimension strictly greater than two, any such compact product must be trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compactness of products and commutators of inner projections Zhang, Peiran Tian, Roumei Lu, Yufeng Yang, Yixin Zu, Chao Functional Analysis Primary 47B38, Secondary 42B30, 30J05 In this paper, we study the compactness of the product and the commutator of two inner projections on the Hardy spaces over the unit disk and the polydisc. For the single-variable case, we provide a complete characterization of the compactness of the commutator of two inner projections by means of Douglas algebra. In the multivariable setting, we discover a rigidity phenomenon: on the bidisc, the product of two inner projections is compact if and only if it has finite rank, whereas on the polydisc of dimension strictly greater than two, any such compact product must be trivial. |
| title | Compactness of products and commutators of inner projections |
| topic | Functional Analysis Primary 47B38, Secondary 42B30, 30J05 |
| url | https://arxiv.org/abs/2604.22284 |