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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2510.14004 |
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| _version_ | 1866915815091077120 |
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| author | Khasnis, Mandar Phatak, Geetanjali Sholapurkar, Vinayak |
| author_facet | Khasnis, Mandar Phatak, Geetanjali Sholapurkar, Vinayak |
| contents | The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a $2$-isometry is subnormal. In this article, we prove that if $μ$ is a sum of unit point mass measures at two non-antipodal points on the unit circle, then the Cauchy dual $M_z'$ of the multiplication operator $M_z$ on the Dirichlet-type space $D(μ)$ is not subnormal. If the points are antipodal then the subnormality of the said operator has been already established in the literature. Thus, we have a complete solution to CDSP in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A solution to the Cauchy dual subnormality problem for a cyclic analytic $2$-isometry with defect operator of rank two Khasnis, Mandar Phatak, Geetanjali Sholapurkar, Vinayak Functional Analysis 47B38, 47B20, 47B32 The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a $2$-isometry is subnormal. In this article, we prove that if $μ$ is a sum of unit point mass measures at two non-antipodal points on the unit circle, then the Cauchy dual $M_z'$ of the multiplication operator $M_z$ on the Dirichlet-type space $D(μ)$ is not subnormal. If the points are antipodal then the subnormality of the said operator has been already established in the literature. Thus, we have a complete solution to CDSP in this case. |
| title | A solution to the Cauchy dual subnormality problem for a cyclic analytic $2$-isometry with defect operator of rank two |
| topic | Functional Analysis 47B38, 47B20, 47B32 |
| url | https://arxiv.org/abs/2510.14004 |