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 |
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