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2003•Proceedings of the American Mathematical SocietyOpen access

A note on the spectrum of an upper triangular operator matrix

Mohamed Barraa, Mohamed Boumazgour

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Abstract

Let $M_C= [\begin {smallmatrix} A& C 0 & B \end {smallmatrix}]$ be a $2\times 2$ upper triangular operator matrix acting on the Banach space $E\oplus F$. We investigate the set of the operators $C$ for which $\sigma (M_C)=\sigma (A)\cup \sigma (B)$, where $\sigma (.)$ denotes the spectrum.

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Let $M_C= [\begin {smallmatrix} A& C 0 & B \end {smallmatrix}]$ be a $2\times 2$ upper triangular operator matrix acting on the Banach space $E\oplus F$. We investigate the set of the operators $C$ for which $\sigma (M_C)=\sigma (A)\cup \sigma (B)$, where $\sigma (.)$ denotes the spectrum.

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Available abstract

Let $M_C= [\begin {smallmatrix} A& C 0 & B \end {smallmatrix}]$ be a $2\times 2$ upper triangular operator matrix acting on the Banach space $E\oplus F$. We investigate the set of the operators $C$ for which $\sigma (M_C)=\sigma (A)\cup \sigma (B)$, where $\sigma (.)$ denotes the spectrum.

Key concepts: Triangular matrix, Spectrum (functional analysis), Sigma, Operator matrix, Operator (biology), Mathematics, Banach space, Matrix (chemical analysis)

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