St. Frunzǎ’s conjecture and strongly decomposable operators. (English) Zbl 0636.47034
Cet article apporte réponse à la conjecture de St. Frunzǎ dont la validité n’était jusqu’a présent pas prouvée: \(\sigma_{T^ Y}(\hat x)=\overline{\sigma_ T(x)\setminus \sigma (T/Y)}\) où Y est un espace maximal spéctral quelconque d’un opérateur T agissant sur un espace de Banach X et x un élément arbitaire de l’espace X. Cette étude a été suivie par un examen approfondi et une caractérisation des opérateurs fortement décomposables.
Reviewer: S.Aliou-Lô
MSC:
| 47B40 | Spectral operators, decomposable operators, well-bounded operators, etc. |
References:
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