Dual Truncated Hankel Operators: Characterization and Properties

2025/10/14 by Arup Chattopadhyay, Chattopadhyay, Arup, Supratim Jana +1
Computer Science · Mathematics · #Matrix Theory and Algorithms #Numerical methods in inverse problems #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2510.12223

Abstract

We introduce the notion of the Dual Truncated Hankel Operator (DTHO) and provide several operator equation characterizations using the dual compressed shift operator. These characterizations are similar to classical results concerning Hankel operators and align with recent findings related to Truncated Hankel Operators (THO) \citeGM. Additionally, our work addresses comprehensive solutions to various operator equations encountered in studying THO and the classical Hankel operator. We have also established some fundamental operator-theoretic properties of DTHO that apply to general symbols and symbols under specific conditions.

Citations

• Liftings and invariant subspaces of Hankel operators
• The dual of the compressed shift
• Invertibility, Fredholmness and kernels of dual truncated Toeplitz\n operators
• Normal Truncated Toeplitz Operators
• Commutation relations for truncated Toeplitz operators
• Truncated Toeplitz operators of finite rank
• Which subnormal Toeplitz operators are either normal or analytic?
• Algebras of truncated Toeplitz operators
• On two problems concerning linear transformations in hilbert space

Related

• On some algebras of truncated Hankel and asymmetric truncated Hankel operators
• Product of truncated Hankel and truncated Toeplitz operators
• Essentially commuting dual truncated Toeplitz operators
• Characterizations of matrix valued asymmetric truncated Hankel operators
• Recent progress on truncated Toeplitz operators