1UFR de Mathématiques, UMR-CNRS 8524 Université de Lille 1 59655 Villeneuve d'Ascq, France 2Departamento de Análisis Matemático Universidad de Granada 18071 Granada, Spain 3Faculté des Sciences Université d'Oujda Oujda, Maroc
Studia Mathematica, Tome 187 (2008) no. 1, pp. 59-73
We study the essential ascent and the related essential ascent spectrum of an
operator on a Banach space. We show that a Banach space $X$ has finite
dimension if and only if the essential ascent of every operator on $X$ is
finite. We also focus on the stability of the essential ascent spectrum under
perturbations, and we prove that an operator $F$ on $X$ has some finite rank
power if and only if $\sigma_{{\rm asc}}^{{\rm e}} (T+F)=\sigma_{{\rm asc}}^{{\rm e}} (T)$ for every operator $T$
commuting with $F$. The quasi-nilpotent part, the analytic core and
the single-valued extension property are also analyzed for
operators with finite
essential ascent.
Keywords:
study essential ascent related essential ascent spectrum operator banach space banach space has finite dimension only essential ascent every operator finite focus stability essential ascent spectrum under perturbations prove operator has finite rank power only sigma asc sigma asc every operator commuting quasi nilpotent part analytic core single valued extension property analyzed operators finite essential ascent
Affiliations des auteurs :
O. Bel Hadj Fredj
1
;
M. Burgos
2
;
M. Oudghiri
3
1
UFR de Mathématiques, UMR-CNRS 8524 Université de Lille 1 59655 Villeneuve d'Ascq, France
2
Departamento de Análisis Matemático Universidad de Granada 18071 Granada, Spain
3
Faculté des Sciences Université d'Oujda Oujda, Maroc
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author = {O. Bel Hadj Fredj and M. Burgos and M. Oudghiri},
title = {Ascent spectrum and essential ascent spectrum},
journal = {Studia Mathematica},
pages = {59--73},
year = {2008},
volume = {187},
number = {1},
doi = {10.4064/sm187-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm187-1-3/}
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AU - M. Burgos
AU - M. Oudghiri
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O. Bel Hadj Fredj; M. Burgos; M. Oudghiri. Ascent spectrum and essential ascent spectrum. Studia Mathematica, Tome 187 (2008) no. 1, pp. 59-73. doi: 10.4064/sm187-1-3
