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

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
Journal	Linear and Multilinear Algebra
DOIs	https://doi.org/10.1080/03081087.2022.2160423
State	Accepted/In press - 2022

Keywords

Sylvester operator equation
hyperinvariant subspace
operator matrices

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10.1080/03081087.2022.2160423

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

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 - 2022

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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

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SN - 0308-1087

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

ER -

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

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Keywords

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