Perturbation of spectra of operator matrices and local spectral theory
By E. Zerouali, H. Zguitti. 2006
58 citations recorded by the source corpus.
Abstract For A ∈ L ( X ) , B ∈ L ( Y ) and C ∈ L ( Y , X ) we denote by M C the operator defined on X ⊕ Y by [ A C 0 B ] . In this article, we study defect set D Σ = ( Σ ( A ) ∪ Σ ( B ) ) ∖ Σ ( M C ) for different spectra including the spectrum, the essential spectrum, Weyl spectrum and the approximate point spectrum. We then apply the obtained results to the stability of such spectra ( D Σ = ∅ ) and the classes of operators C for which stability holds of M C using local spectral theory.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0d06673cc0923e1b64b57a057bfac456fa30e1ea
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Essential point spectra of operator matrices trough local spectral theory (2008, background): “Since A, A∗, B and B∗ satisfy the SVEP then it follows from [7,9,13] that”