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PERTURBATION OF POINT SPECTRA OF 2×2 UPPER TRIANGULAR OPERATOR MATRICES

Huang Junji

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Abstract

Perturbation of four kinds of point spectrum of 2×2 upper triangular operator matrices is studied.Based on the space decomposition technique and the subdivision of point spectrum and residual spectrum,a necessary and sufficient condition of σ_(pi)(M_C) = σ_(pi)(A) ∪σ_(pi)(B)(i = 1,2,3,4) for every bounded operator C is obtainedn by using its diagonal elements.

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Perturbation of four kinds of point spectrum of 2×2 upper triangular operator matrices is studied.Based on the space decomposition technique and the subdivision of point spectrum and residual spectrum,a necessary and sufficient condition of σ_(pi)(M_C) = σ_(pi)(A) ∪σ_(pi)(B)(i = 1,2,3,4) for every bounded operator C is obtainedn by using its diagonal elements.

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Available abstract

Perturbation of four kinds of point spectrum of 2×2 upper triangular operator matrices is studied.Based on the space decomposition technique and the subdivision of point spectrum and residual spectrum,a necessary and sufficient condition of σ_(pi)(M_C) = σ_(pi)(A) ∪σ_(pi)(B)(i = 1,2,3,4) for every bounded operator C is obtainedn by using its diagonal elements.

Key concepts: Triangular matrix, Mathematics, Operator matrix, Diagonal, Perturbation (astronomy), Spectrum (functional analysis), Operator (biology), Bounded function

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