a-Weyl's theorem and the single valued extension property

• Autores: Mourad Oudghiri
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 1, 2006, págs. 41-50
• Idioma: inglés
• Títulos paralelos:
  • El teorema de a-Weyl y la propiedad de extensión univaluada
• Enlaces
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• Resumen

  • In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f Î H(s(T)). We also provide several conditions that force an operator with the SVEP to obey a-Weyl's theorem.

    The author would like to precise that this paper constitute a part of his thesis [16].