Propriétés Spectrales Locales D'une Matrice Carrée des Opérateurs

M. Houimdi et H. Zguitti

Abstract

        If X and Y are complex Banach spaces,then for A Î {\Cal L}(X)BÎ{\Cal L}(Y) and CÎ{\Cal L}(Y,X)  we denote by  MC  the operator defined on  X Å Y  by

MC  =  matrix

A      C

0        B


When B has SVEP, we show that σ(
MC) = σ(A) È B for all C Î {\Cal L}(Y,X)  And in the Hilbert space setting, this result gives a partial positive answer to the question 3 posed in [5].