Geodesic
Self-adjoint perturbations of left (right) weyl spectrum for upper triangular operator matrices
Filomat, Tome 36 (2022) no. 13, p. 4385

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DOI

Let H be a separable infinite-dimensional Hilbert space. Given the operators A ∈ B(H) and B ∈ B(H), we define M X := A X 0 B where X ∈ S(H) is a self-adjoint operator. In this paper, a necessary and sufficient condition is given for M X to be a left (right) Weyl operator for some X ∈ S(H). Moreover, it is shown that X∈S(H) σ ⋆ (M X) = X∈S(H)∩Inv(H) σ ⋆ (M X) = X∈B(H) σ ⋆ (M X) ∪ ∆, where σ * is the left (right) Weyl spectrum. Finally, we further characterize the perturbation of the left (right) Weyl spectrum for Hamiltonian operators.
DOI : 10.2298/FIL2213385W
Classification : 47A53, 47A55, 47B99
Keywords: upper triangular operator matrix, self-adjoint operator, left (right) Weyl operator, Hamiltonian operator 
Xiufeng Wu; Junjie Huang; Alatancang Chen. Self-adjoint perturbations of left (right) weyl spectrum for upper triangular operator matrices. Filomat, Tome 36 (2022) no. 13, p. 4385 . doi: 10.2298/FIL2213385W
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     title = {Self-adjoint perturbations of left (right) weyl spectrum for upper triangular operator matrices},
     journal = {Filomat},
     pages = {4385 },
     year = {2022},
     volume = {36},
     number = {13},
     doi = {10.2298/FIL2213385W},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2213385W/}
}
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