On the perturbation functions and similarity orbits

Haïkel Skhiri

Haïkel Skhiri

Studia Mathematica, Tome 187 (2008), p. 57-66 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that the essential spectral radius $ϱ_{e} (T)$ of T ∈ B(H) can be calculated by the formula $ϱ_{e} (T)$ = inf $ℱ_{♯ \cdot ♯} (X T X^{- 1})$ : X an invertible operator, where $ℱ_{♯ \cdot ♯} (T)$ is a Φ₁-perturbation function introduced by Mbekhta [J. Operator Theory 51 (2004)]. Also, we show that if $_{♯ \cdot ♯} (T)$ is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then $d i s t (0, σ_{e} (T))$ = sup $_{♯ \cdot ♯} (X T X^{- 1})$ : X an invertible operator.

Publié le : 2008-01-01

Zbl 1146.47008

EUDML-ID : urn:eudml:doc:285201

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Haïkel Skhiri. On the perturbation functions and similarity orbits. Studia Mathematica, Tome 187 (2008) pp. 57-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm188-1-3/