%0 Journal Article
%T Local spectral theory for  operator matrices
%A H. Elbjaoui
%A E. H. Zerouali
%J International Journal of Mathematics and Mathematical Sciences
%D 2003
%I Hindawi Publishing Corporation
%R 10.1155/s0161171203012043
%X We discuss the spectral properties of the operator MC∈ℒ(X⊕Y) defined by MC:=(AC0B), where A∈ℒ(X), B∈ℒ(Y), C∈ℒ(Y,X), and X, Y are complex Banach spaces. We prove that (SA∗∩SB)∪σ(MC)=σ(A)∪σ(B) for all C∈ℒ(Y,X). This allows us to give a partial positive answer to Question 3 of Du and Jin (1994) and generalizations of some results of Houimdi and Zguitti (2000). Some applications to the similarity problem are also given.
%U http://www.hindawi.com/journals/ijmms/2003/893151/abs/