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

Mourad Oudghiri

• 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].