Geodesic
Extended eigenvalues of a closed linear operator
Filomat, Tome 36 (2022) no. 13, p. 4277

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DOI

A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator B such that AB = λBA. In this case, B is said to be an eigenoperator. This research paper is devoted to the investigation of some results of extended eigenvalues for a closed linear operator on a complex Banach space. The obtained results are explored in terms two cases bounded, and closed eigenoperators. In addition, the notion of extended eigenvalues for a 2 × 2 upper triangular operator matrix is introduced and some of its properties are displayed.
DOI : 10.2298/FIL2213277A
Classification : 11B05, 47A53, 39B42
Keywords: Extended eigenvalue, Eigenoperator, Essential spectrum, 2 × 2 Block matrix 
Aymen Ammar; Fatima Zohra Boutaf; Aref Jeribi. Extended eigenvalues of a closed linear operator. Filomat, Tome 36 (2022) no. 13, p. 4277 . doi: 10.2298/FIL2213277A
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     title = {Extended eigenvalues of a closed linear operator},
     journal = {Filomat},
     pages = {4277 },
     year = {2022},
     volume = {36},
     number = {13},
     doi = {10.2298/FIL2213277A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2213277A/}
}
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