Subnormal block Toeplitz operators

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

doi:10.1007/s11854-025-0358-3

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Subnormal block Toeplitz operators

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

Journal d'analyse mathématique (Jerusalem), Vol.155(2), pp.485-500

04/2025

DOI: 10.1007/s11854-025-0358-3

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Abstract

In this paper we consider the subnormality of block Toeplitz operators T, where is an n × n matrix-valued function on the unit circle T of the form = Q∗ (Q is a finite Blaschke–Potapov product). This is related to a matrix-valued version of Halmos’ Problem 5 and the Nakazi–Takahashi Theorem. We ask whether T is either normal or analytic if T is subnormal, where 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 ∗ is not of bounded type

Details

Title: Subtitle: Subnormal block Toeplitz operators
Creators: Mankunikuzhiyil Abhinand - University of Calicut
Raúl E. Curto - University of Iowa
In Sung Hwang - Sungkyunkwan University
Woo Young Lee - Korea Institute for Advanced Study
Thankarajan Prasad - University of Calicut
Resource Type: Journal article
Publication Details: Journal d'analyse mathématique (Jerusalem), Vol.155(2), pp.485-500
DOI: 10.1007/s11854-025-0358-3
ISSN: 0021-7670
eISSN: 1565-8538
Publisher: HEBREW UNIV MAGNES PRESS; JERUSALEM
Grant note: Junior Research Fellowship, University Grant commission, Government of IndiaNRF(Korea): 2021R1A2C1005428 Mathematical Research Impact Centric Support, MATRICS: MTR/2021/000373 SERB, Department of Science and Technology (DST), Government of India
The authors are grateful to the Referee for a detailed reading of the paper and for helpful suggestions. The first-named author (Abhinand M.) was supported by the Junior Research Fellowship, University Grant commission, Government of India. The third-named author (I. S. Hwang) was supported by NRF(Korea) grant No. 2022R1A2C1010830. The fourth-named author (W. Y. Lee) was supported by NRF(Korea) grant No. 2021R1A2C1005428. The fifth-named author (Prasad T.) was supported in part by the Mathematical Research Impact Centric Support, MATRICS (MTR/2021/000373) by SERB, Department of Science and Technology (DST), Government of India.
Language: English
Electronic publication date: 01/21/2025
Date published: 04/2025
Academic Unit: Mathematics
Record Identifier: 9984781273002771

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