On the perturbation functions and similarity orbits

Haïkel Skhiri. "On the perturbation functions and similarity orbits." Studia Mathematica 188.1 (2008): 57-66. <http://eudml.org/doc/285201>.

@article{HaïkelSkhiri2008,
abstract = {We show that the essential spectral radius $ϱ_\{e\}(T)$ of T ∈ B(H) can be calculated by the formula $ϱ_\{e\}(T)$ = inf$ℱ_\{♯·♯\}(XTX^\{-1\})$: X an invertible operator, where $ℱ_\{♯·♯\}(T)$ is a Φ₁-perturbation function introduced by Mbekhta [J. Operator Theory 51 (2004)]. Also, we show that if $_\{♯·♯\}(T)$ is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then $dist(0,σ_\{e\}(T))$ = sup$_\{♯·♯\}(XTX^\{-1\})$: X an invertible operator.},
author = {Haïkel Skhiri},
journal = {Studia Mathematica},
keywords = {Fredholm operator; essential spectrum; essential spectral radius; Calkin algebra; similarity orbit},
language = {eng},
number = {1},
pages = {57-66},
title = {On the perturbation functions and similarity orbits},
url = {http://eudml.org/doc/285201},
volume = {188},
year = {2008},
}

TY - JOUR
AU - Haïkel Skhiri
TI - On the perturbation functions and similarity orbits
JO - Studia Mathematica
PY - 2008
VL - 188
IS - 1
SP - 57
EP - 66
AB - We show that the essential spectral radius $ϱ_{e}(T)$ of T ∈ B(H) can be calculated by the formula $ϱ_{e}(T)$ = inf$ℱ_{♯·♯}(XTX^{-1})$: X an invertible operator, where $ℱ_{♯·♯}(T)$ is a Φ₁-perturbation function introduced by Mbekhta [J. Operator Theory 51 (2004)]. Also, we show that if $_{♯·♯}(T)$ is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then $dist(0,σ_{e}(T))$ = sup$_{♯·♯}(XTX^{-1})$: X an invertible operator.
LA - eng
KW - Fredholm operator; essential spectrum; essential spectral radius; Calkin algebra; similarity orbit
UR - http://eudml.org/doc/285201
ER -