Factorization of Hankel operators, range inclusion of Toeplitz and Hankel operators on the vector-valued Hardy space

Sudip Ranjan Bhuia

doi:10.5802/crmath.680

Research article - Functional analysis, Operator theory

Factorization of Hankel operators, range inclusion of Toeplitz and Hankel operators on the vector-valued Hardy space

Sudip Ranjan Bhuia ¹

¹ Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560 059, India

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1773-1778.

Abstract
Résumé

Using Douglas theorem on factorization and range inclusion of bounded linear operators, we give the factorization of Hankel operators, range inclusion of Hankel and Toeplitz operators defined on vector-valued Hardy spaces.

En utilisant le théorème de Douglas sur la factorisation impliquée par l’inclusion des images de deux opérateurs linéaires bornés, nous donnons la factorisation des opérateurs de Hankel quand il y a inclusion des images de deux opérateurs de Hankel ou de Toeplitz définis sur des espaces de Hardy à valeur vectorielle.

Received: 2024-05-01
Revised: 2024-08-20
Accepted: 2024-08-20
Published online: 2024-11-25

Zbl

DOI: 10.5802/crmath.680

Classification: 47A56, 47A63, 47A68, 47B20, 47B35
Keywords: Toeplitz operators, Hankel operators, Hardy space, inner functions, Douglas Lemma, factorization, majorization
Mots-clés : Opérateurs de Toeplitz, opérateurs de Hankel, espace de Hardy, fonctions intérieures, lemme de Douglas, factorisation, majorisation

Author's affiliations:

Sudip Ranjan Bhuia ¹

¹ Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560 059, India

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Sudip Ranjan Bhuia},
     title = {Factorization of {Hankel} operators, range inclusion of {Toeplitz} and {Hankel} operators on the vector-valued {Hardy} space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1773--1778},
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Sudip Ranjan Bhuia. Factorization of Hankel operators, range inclusion of Toeplitz and Hankel operators on the vector-valued Hardy space. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1773-1778. doi : 10.5802/crmath.680. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.680/

References
Cited by

[1] Hari Bercovici Operator theory and arithmetic in $H^{\infty}$ , Mathematical Surveys and Monographs, 26, American Mathematical Society, 1988, xii+275 pages | DOI | MR | Zbl

[2] R. G. Douglas On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Am. Math. Soc., Volume 17 (1966), pp. 413-415 | DOI | MR | Zbl

[3] Robert B. Leech Factorization of analytic functions and operator inequalities, Integral Equations Oper. Theory, Volume 78 (2014) no. 1, pp. 71-73 | DOI | MR | Zbl

[4] B. A. Lotto Range inclusion of Toeplitz and Hankel operators, J. Oper. Theory, Volume 24 (1990) no. 1, pp. 17-22 | MR | Zbl

[5] Béla Sz.-Nagy; Ciprian Foias; Hari Bercovici; László Kérchy Harmonic analysis of operators on Hilbert space, Universitext, Springer, 2010, xiv+474 pages | DOI | MR | Zbl

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