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A note on the spectrum of an upper triangular operator matrix

Authors:	Mohamed Barraa Mohamed Boumazgour

Institution:	Département de Mathématiques, Faculté des Sciences Semlalia, B.P 2390, Marrakech, Maroc ; Département de Mathématiques, Faculté des Sciences Semlalia, B.P 2390, Marrakech, Maroc

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 for which $\sigma(M_C)=\sigma(A)\cup\sigma(B)$ , where $\sigma(.)$ denotes the spectrum.

Keywords:	Spectrum $2\times 2$ upper triangular operator matrix generalized derivation

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