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Sur la théorie spectrale locale des shifts à poids opérateurs

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  • Mohamed Houimdi
  • Hassane Zguitti

Abstract

Nous étudions les propriétés spectrales locales du shift unilateral à poids opérateurs. Nous donnons une condition nécessaire et suffisante pour que l'adjoint satisfasse la propriété de l'extension unique (SVEP). Une condition suffisante pour satisfaire la propriété de Dunford ( C ) ainsi qu'une condition nécessaire pour satisfaire la condition de Bishop ( β ) seront données. Enfin, nous montrons que le shift à poids opérateurs est décomposable si, et seulement si, il est quasinilpotent. We study the local spectral properties for the unilateral shift with operator-valued weights. We give necessary and sufficient conditions for the adjoint to satisfy the SVEP. Sufficient condition to satisfy Dunford's property ( C ) and necessary condition to satisfy Bishop's condition ( β ) are given. Finally we show that the unilateral shift with operator-valued weights is decomposable if and only if it is quasinilpotent.

Suggested Citation

  • Mohamed Houimdi & Hassane Zguitti, 2005. "Sur la théorie spectrale locale des shifts à poids opérateurs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:201452
    DOI: 10.1155/IJMMS.2005.3497
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