Abstract. In this article we study left and right poles of the resolvent of a bounded operator defined on an infinite-dimensional complex Banach space. In particular, some spectral decompositions associated with left and right poles of the resolvent are established, and the components of the upper and lower semi B-Fredholm regions are studied by means of the localized single valued extension property.

AMS Subject Classification (1991): 47A10, 47A11; 47A53, 47A55

Keyword(s): localized SVEP, B, semi-Browder operators, semi B-Weyl operators, left and right Drazin invertibility

Received October 2, 2007, and in revised form December 17, 2007. (Registered under 6039/2009.)