Local Spectral Theory and Surjective Spectrum of Linear Relations

2021 ◽  
Author(s):  
M. Mnif ◽  
A.-A. Ouled-Hmed
Keyword(s):  
Spectral Theory ◽  
Linear Relations ◽  
Local Spectral Theory

The Local Spectral Theory for Linear Relations Involving SVEP

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Aymen Ammar ◽  
Ameni Bouchekoua ◽  
Aref Jeribi
Keyword(s):  
Spectral Theory ◽  
Linear Relations ◽  
Local Spectral Theory

scholarly journals The Local spectral theory and surjective spectrum of linear relations

2021 ◽  
Vol 73 (2) ◽  
pp. 222-237
Author(s):  
M. Mnif ◽  
A.-A. Ouled-Hmed
Keyword(s):  
Banach Space ◽  
Spectral Theory ◽  
Linear Relation ◽  
Local Spectrum ◽  
Linear Relations ◽  
Analytic Core ◽  
Local Spectral Theory

UDC 517.98 This paper initiates a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core and quasinilpotent part of a linear relation in a Banach space . As an application, we give a characterization of the surjective spectrum in terms of the local spectrum and show that if , then does not cluster at .

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
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