Subnormal block Toeplitz operators

Mankunikuzhiyil Abhinand; Raul E Curto; In Sung Hwang; Woo Young Lee; Thankarajan Prasad

doi:10.48550/arxiv.2605.02186

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Subnormal block Toeplitz operators

Mankunikuzhiyil Abhinand, Raul E Curto, In Sung Hwang, Woo Young Lee and Thankarajan Prasad

ArXiv.org

Cornell University

05/04/2026

DOI: 10.48550/arxiv.2605.02186

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this paper we consider the subnormality of block Toeplitz operators TΦ, where Φ is an n × n matrix-valued function on the unit circle T of the form Φ = QΦ∗ (Q is a finite Blaschke–Potapov product). This is related to a matrix-valued version of Halmos’s Problem 5 and Nakazi-Takahashi Theorem. We ask whether TΦ is either normal or analytic if TΦ is subnormal, where Φ is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when Φ∗ is not of bounded type

Mathematics - Functional Analysis

Details

Title: Subtitle: Subnormal block Toeplitz operators
Creators: Mankunikuzhiyil Abhinand
Raul E Curto
In Sung Hwang
Woo Young Lee
Thankarajan Prasad
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2605.02186
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 05/04/2026
Academic Unit: Mathematics
Record Identifier: 9985161446102771

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