A solution to the Cauchy dual subnormality problem for a cyclic analytic $2$-isometry with defect operator of rank two
Functional Analysis
2026-02-26 v2
Abstract
The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a -isometry is subnormal. In this article, we prove that if is a sum of unit point mass measures at two non-antipodal points on the unit circle, then the Cauchy dual of the multiplication operator on the Dirichlet-type space 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.
Cite
@article{arxiv.2510.14004,
title = {A solution to the Cauchy dual subnormality problem for a cyclic analytic $2$-isometry with defect operator of rank two},
author = {Mandar Khasnis and Geetanjali Phatak and Vinayak Sholapurkar},
journal= {arXiv preprint arXiv:2510.14004},
year = {2026}
}