Authors: | Đorđević, Bogdan | Affiliations: | Mathematics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Singular Sylvester equation in Banach spaces and its applications: Fredholm theory approach | Journal: | Linear Algebra and Its Applications | Volume: | 622 | First page: | 189 | Last page: | 214 | Issue Date: | 1-Aug-2021 | Rank: | ~M21 | ISSN: | 0024-3795 | DOI: | 10.1016/j.laa.2021.03.035 | Abstract: | We prove that, by assuming the existence of at least one left upper semi-Fredholm operator, then under some natural conditions, the singular operator equation AX−XB=C is solvable if the appropriate matrix equation is solvable. This characterization is convenient because the matrix version of the problem has been closed in [14] and [17]. In addition, we obtain sufficient conditions for A, B and X such that the generalized derivation AX−XB is a compact operator. A connection is established with Fréchet derivatives and commutators of idempotents. Applications to Schur coupling and linear time-invariant systems are mentioned. |
Keywords: | Fredholm theory | Operator algebras | Sylvester equations | Publisher: | Elsevier | Project: | Functional analysis, stochastic analysis and applications |
Show full item record
SCOPUSTM
Citations
11
checked on Dec 20, 2024
Page view(s)
37
checked on Dec 22, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.