Ascent spectrum and essential ascent spectrum

O. Bel Hadj Fredj, M. Burgos, and M. Oudghiri. "Ascent spectrum and essential ascent spectrum." Studia Mathematica 187.1 (2008): 59-73. <http://eudml.org/doc/284537>.

@article{O2008,
abstract = {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 $σ_\{asc\}^\{e\}(T + F) = σ_\{asc\}^\{e\}(T)$ 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.},
author = {O. Bel Hadj Fredj, M. Burgos, M. Oudghiri},
journal = {Studia Mathematica},
keywords = {spectrum; ascent; essential ascent; perturbation; semi-Fredholm},
language = {eng},
number = {1},
pages = {59-73},
title = {Ascent spectrum and essential ascent spectrum},
url = {http://eudml.org/doc/284537},
volume = {187},
year = {2008},
}

TY - JOUR
AU - O. Bel Hadj Fredj
AU - M. Burgos
AU - M. Oudghiri
TI - Ascent spectrum and essential ascent spectrum
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 1
SP - 59
EP - 73
AB - 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 $σ_{asc}^{e}(T + F) = σ_{asc}^{e}(T)$ 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.
LA - eng
KW - spectrum; ascent; essential ascent; perturbation; semi-Fredholm
UR - http://eudml.org/doc/284537
ER -