Geodesic
Quasi-Fredholm spectrum for operator matrices
Filomat, Tome 36 (2022) no. 14, p. 4893

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DOI

For A ∈ L(X), B ∈ L(Y) and C ∈ L(Y,X) we denote by MC the operator matrix defined on X ⊕ Y by MC = ( A C 0 B ) . In this paper, we prove that σqF(A) ∪ σqF(B) ⊊ ⋃ C∈L(Y,X) σqF(MC) ∪ σp(B) ∪ σp(A∗), where σqF(.) (resp. σp(.)) denotes the quasi-Fredholm spectrum (resp. the point spectrum). Furthermore, we consider some sufficient conditions for MC to be quasi-Fredholm and sufficient conditions to have σqF(A) ∪ σqF(B) = ⋂ C∈L(Y,X) σqF(MC).
DOI : 10.2298/FIL2214893E
Classification : 47A53, 47A10
Keywords: Operator matrices, Quasi-Fredholm operator, Quasi-Fredholm spectrum 
I El Ouali; M Ech-Cherif El Kettani; M Karmouni. Quasi-Fredholm spectrum for operator matrices. Filomat, Tome 36 (2022) no. 14, p. 4893 . doi: 10.2298/FIL2214893E
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     author = {I El Ouali and M Ech-Cherif El Kettani and M Karmouni},
     title = {Quasi-Fredholm spectrum for operator matrices},
     journal = {Filomat},
     pages = {4893 },
     year = {2022},
     volume = {36},
     number = {14},
     doi = {10.2298/FIL2214893E},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2214893E/}
}
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