An example of a cyclic analytic $2$-isometry with defect operator of rank $3$, whose Cauchy dual is not subnormal
Functional Analysis
2025-11-07 v1
Abstract
The Cauchy dual subnormality problem (CDSP, for short) asks whether the Cauchy dual of a isometry is subnormal. In this article, we provide a counter-example to CDSP by constructing a cyclic, analytic, isometry whose defect operator is of rank . In particular, we prove that the Cauchy dual of the multiplication operator on the Dirichlet space is not subnormal if is supported at three equi-spaced points on the unit circle.
Keywords
Cite
@article{arxiv.2511.04565,
title = {An example of a cyclic analytic $2$-isometry with defect operator of rank $3$, whose Cauchy dual is not subnormal},
author = {Saee A. Joshi and Geetanjali M. Phatak and Vinayak M. Sholapurkar},
journal= {arXiv preprint arXiv:2511.04565},
year = {2025}
}