2023/08/02 by Senhua Zhu, Zhu, Senhua, Yufeng Lu +3
Mathematics · #46E40 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47B35 #Secondary 47B20
paper · pdf · doi:10.48550/arxiv.2308.01373
openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we continue Curto-Hwang-Lee's work to study 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 hyponormality and subnormality of 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 extended Curto-Hwang-Lee's result to block Toeplitz operators with symbols of bounded type. More precisely, we proved that if Ψ,Ψ∗ are matrix-valued functions of bounded type and the inner part of Ψ of Douglas-Shapiro-Shields factorization is a scalar inner function, then every hyponormal Toeplitz operator TΨ whose square is also hyponormal must be either normal or analytic.