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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.04565 |
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Table of Contents:
- The Cauchy dual subnormality problem (CDSP, for short) asks whether the Cauchy dual of a $2-$isometry is subnormal. In this article, we provide a counter-example to CDSP by constructing a cyclic, analytic, $2-$isometry whose defect operator is of rank $3$. In particular, we prove that the Cauchy dual $M_z'$ of the multiplication operator $M_z$ on the Dirichlet space $D(μ)$ is not subnormal if $μ$ is supported at three equi-spaced points on the unit circle.