A solution to the Cauchy dual subnormality problem for a cyclic analytic 2-isometry with defect operator of rank two

2025/10/15 by Khasnis, Mandar, Phatak, Geetanjali, Sholapurkar, Vinayak · 1 citation
#47B20 #47B32 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.14004

Abstract

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 linear combination 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 space D(μ) is not subnormal. If the two points are antipodal then the subnormality of the said operator has been already established in the literature. Thus, we have a complete solution of CDSP in this case.

Citations

• The Cauchy dual subnormality problem via de Branges-Rovnyak spaces
• The Cauchy dual subnormality problem for cyclic 2-isometries
• Taylor spectrum approach to Brownian-type operators with quasinormal entry
• A solution to the Cauchy dual subnormality problem for 2-isometries
• de Branges-Rovnyak spaces: basics and theory
• De Branges–Rovnyak spaces and Dirichlet spaces
• Local Dirichlet spaces as de Branges-Rovnyak spaces

Cited by

• An example of a cyclic analytic 2-isometry with defect operator of rank 3, whose Cauchy dual is not subnormal

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