On the generalized Sylvester operator equation AX−Y B = C

Il Ju An; Eungil Ko; Ji Eun Lee

doi:10.1080/03081087.2022.2160423

On the generalized Sylvester operator equation AX−Y B = C

Il Ju An, Eungil Ko, Ji Eun Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we study the necessary and sufficient conditions to have a solution pair (Formula presented.) to the generalized Sylvester equation AX−Y B = C where (Formula presented.) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair (Formula presented.) of the operator equation AX−Y B = C. Finally, we consider some properties of the operator equation AX−Y B = C when A and B belong to the special classes of operators.

Original language	English
Pages (from-to)	585-596
Number of pages	12
Journal	Linear and Multilinear Algebra
Volume	72
Issue number	4
DOIs	https://doi.org/10.1080/03081087.2022.2160423
State	Published - 2024

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© 2022 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Sylvester operator equation
hyperinvariant subspace
operator matrices

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10.1080/03081087.2022.2160423

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abstract = "In this paper, we study the necessary and sufficient conditions to have a solution pair (Formula presented.) to the generalized Sylvester equation AX−Y B = C where (Formula presented.) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair (Formula presented.) of the operator equation AX−Y B = C. Finally, we consider some properties of the operator equation AX−Y B = C when A and B belong to the special classes of operators.",

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AU - An, Il Ju

AU - Ko, Eungil

AU - Lee, Ji Eun

PY - 2024

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N2 - In this paper, we study the necessary and sufficient conditions to have a solution pair (Formula presented.) to the generalized Sylvester equation AX−Y B = C where (Formula presented.) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair (Formula presented.) of the operator equation AX−Y B = C. Finally, we consider some properties of the operator equation AX−Y B = C when A and B belong to the special classes of operators.

AB - In this paper, we study the necessary and sufficient conditions to have a solution pair (Formula presented.) to the generalized Sylvester equation AX−Y B = C where (Formula presented.) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair (Formula presented.) of the operator equation AX−Y B = C. Finally, we consider some properties of the operator equation AX−Y B = C when A and B belong to the special classes of operators.

KW - Sylvester operator equation

KW - hyperinvariant subspace

KW - operator matrices

UR - https://www.scopus.com/pages/publications/85145336701

U2 - 10.1080/03081087.2022.2160423

DO - 10.1080/03081087.2022.2160423

M3 - Article

AN - SCOPUS:85145336701

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SP - 585

EP - 596

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 4

ER -

On the generalized Sylvester operator equation AX−Y B = C

Abstract

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Keywords

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