scholarly journals Local spectral theory for2×2operator matrices

2003 ◽  
Vol 2003 (42) ◽  
pp. 2667-2672 ◽  
Author(s):  
H. Elbjaoui ◽  
E. H. Zerouali
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Spectral Properties ◽  
Positive Answer ◽  
Sigma B ◽  
Similarity Problem ◽  
Local Spectral Theory

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.

scholarly journals Five short lemmas in Banach spaces

2016 ◽  
Vol 32 (1) ◽  
pp. 131-140
Author(s):  
QINGPING ZENG ◽  
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Commutative Diagram ◽  
Spectral Properties ◽  
Linear Operators ◽  
General Question ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Local Spectral Theory

Consider a commutative diagram of bounded linear operators between Banach spaces...with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory.

scholarly journals Local Spectral Theory for R and S Satisfying RnSRn = Rj

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 120
Author(s):  
Salvatore Triolo
Keyword(s):  
Spectral Theory ◽  
Spectral Properties ◽  
Operator Equations ◽  
The Relationship ◽  
Local Spectral Theory

In this paper, we analyze local spectral properties of operators R,S and RS which satisfy the operator equations RnSRn=Rj and SnRSn=Sj for same integers j≥n≥0. We also continue to study the relationship between the local spectral properties of an operator R and the local spectral properties of S. Thus, we investigate the transmission of some local spectral properties from R to S and we illustrate our results with an example. The theory is exemplified in some cases.

scholarly journals The Kato-type spectrum and local spectral theory

2007 ◽  
Vol 57 (3) ◽  
pp. 831-842 ◽  
Author(s):  
T. L. Miller ◽  
V. G. Miller ◽  
M. M. Neumann
Keyword(s):  
Spectral Theory ◽  
Type Spectrum ◽  
Local Spectral Theory

$B$-spectral theory of linear relations in complex Banach spaces

2017 ◽  
Vol 91 (3-4) ◽  
pp. 455-466
Author(s):  
Marcel Roman ◽  
Adrian Sandovici
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Linear Relations
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