On the perturbation functions and similarity orbits

• Autorzy: Haïkel Skhiri
• Języki publikacji: EN

Abstrakty

EN

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 $𝒢_{♯·♯}(T)$ is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then $dist(0,σ_{e}(T))$ = sup{$𝒢_{♯·♯}(XTX^{-1})$: X an invertible operator}.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 47A53: (Semi-) Fredholm operators; index theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 188
• Numer: 1
• Strony: 57-66

Daty

wydano

2008

Twórcy

autor

Haïkel Skhiri

• Département de Mathématiques, Faculté des Sciences de Monastir, Avenue de l'environnement, 5019 Monastir, Tunisie

Identyfikatory

DOI

10.4064/sm188-1-3