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].