Year: 2025
Type: article
Abstract: We continue Curto–Hwang–Lee’s study of the connection between hyponormality and subnormality for block Toeplitz operators acting on the vector-valued Hardy space of the unit circle. Curto–Hwang–Lee’s work focuses primarily on block Toeplitz operators with rational symbols. By studying the greatest common divisor of matrix-valued inner functions and the “weak” commutativity of matrix-valued inner functions, we extend Curto–Hwang–Lee’s result to block Toeplitz operators with symbols of bounded type. More precisely, we prove that if Ψ,Ψ∗ are matrix-valued functions of bounded type and the inner part of the Douglas–Shapiro–Shields factorization of Ψ is a scalar inner function, then every hyponormal Toeplitz operator TΨ whose square is also hyponormal must be either normal or analytic.
Source: Studia Mathematica
Authors: Senhua Zhu, Yufeng Lu, Chao Zu
Institutions: Shantou University, Dalian University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1656184991, G4339109340
OpenAlex ID: W4413130126