2012•Advances in MathematicsRequires access

On the Perturbation of the Spectra of Kato Upper Triangular Operator Matrices

Tian Junhong, Xiaohong Cao

Abstract

Letσ_2(A) =σ_e(A)∪σ_k(A) U{λ∈C:ind(A-λI) 0},whereσ_e(A) andσ_k(A) denote the essential spectrum and Kato spectrum of an operator A,respectively.In thispaper,using the relation between the nullity and the defect of a given pair operators,we studythe perturbation of the spectrumσ_2(-) for upper triangular operator matrices.

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Key concepts: Mathematics, Operator matrix, Perturbation (astronomy), Spectrum (functional analysis), Operator (biology), Triangular matrix, Eigenvalues and eigenvectors, Spectral line