Abstract
Given a closed operatorA acting in a Banach spaceX, we define the regular (respectively the essentialy regular) spectrum σ r (A) (respectively σ e,r (A)) ofA. We prove that σ r (A) and σ e,r (A) are a closed subsets of the classical spectrum σ(A) ofA. Morever ifA is bounded we prove that σ r (A) and σ e,r (A)) satisfies the spectral mapping theorem.
Résumé
Etant donné un opérateur fermé dans un espace de BanachX, nous définissons le spectre régulier (respectivement essentiellement régulier) σ r (A)) (respectivement σ e,r (A)) deA. Nous montrerons que σ r (A) et σ e,r (A) sont des sous-ensembles fermés du spectre classique σ(A) deA. Si en plusA est borné, nous montrons que σ r (A) et σ e,r (A) verifient le théorème de l’application spectrale.
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Berkani, M., Ouahab, A. Operateurs essentiellement reguliers dans les espaces de Banach. Rend. Circ. Mat. Palermo 46, 131–160 (1997). https://doi.org/10.1007/BF02844478
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DOI: https://doi.org/10.1007/BF02844478
Mots cles
- Opérateur régulier
- Opérateur essentiellement régulier
- spectre régulier
- spectre essentiellement régulier
- conorme