Local spectrum and local spectral radius of an operator at a fixed vector

Janko Bračič; Vladimír Müller

Studia Mathematica, Tome 192 (2009), p. 155-162 / Harvested from The Polish Digital Mathematics Library

Résumé

Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() with $σ_{T} (e) = σ_{δ} (T)$ , respectively $r_{T} (e) = r (T)$ , is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.

Publié le : 2009-01-01

Zbl 1182.47004

EUDML-ID : urn:eudml:doc:286117

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Janko Bračič; Vladimír Müller. Local spectrum and local spectral radius of an operator at a fixed vector. Studia Mathematica, Tome 192 (2009) pp. 155-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-3/