Affiliation:
1. Département de Mathématiques et Informatique, Faculté des Sciences de Rabat, Université Mohamed V, Rabat BP 1014, Morocco
Abstract
We discuss the spectral properties of the operatorMC∈ℒ(X⊕Y)defined byMC:=(AC0B), whereA∈ℒ(X),B∈ℒ(Y),C∈ℒ(Y,X), andX,Yare complex Banach spaces. We prove that(SA∗∩SB)∪σ(MC)=σ(A)∪σ(B)for allC∈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.
Subject
Mathematics (miscellaneous)
Cited by
17 articles.
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