Saved in:
Bibliographic Details
Main Authors: Joshi, Saee A., Phatak, Geetanjali M., Sholapurkar, Vinayak M.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.04565
Tags: Add Tag
No Tags, Be the first to tag this record!
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.