A Note on Drazin Invertibility for Upper Triangular Block
Operators
H. Zguitti
A bounded linear operator A acting on a Banach space X is said to be an upper
triangular block operators of order n, and we write A ∈ UT n (X), if there exists a
decomposition of X = X1 ⊕ · · · ⊕ Xn and an n × n matrix operator (Ai,j )1≤i,j≤n such
that A = (Ai,j )1≤i,j≤n , Ai,j = 0 for i > j. In this note we characterize a large set of
n
[
entries Ai,j with j > i such that σD (A) =
σD (Ai,i ); where σD (.) is the Drazin speci=1
trum. Some applications concerning the Fredholm theory and meromorphic operators
are given.
Faculté Pluridisciplinaire De Nador, Université Mohammed I, Morocco
[email protected]