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On the equivalence of Browder’s and generalized Browder’s theorem. (English) Zbl 1097.47012
M. Berkani and J. J. Koliha [Acta Sci. Math. 69, No. 1–2, 359–376 (2003; Zbl 1050.47014)] proved that the generalized Browder’s (resp., the generalized $$a$$-Browder’s) theorem implies Browder’s (resp., $$a$$-Browder’s) theorem for a Banach space operator. In the present paper, the authors show that the generalized Browder’s (resp., the generalized $$a$$-Browder’s) theorem holds for a Banach space operator if and only if Browder’s (resp., $$a$$-Browder’s) theorem does. They also give conditions under which the generalized Weyl’s (resp., generalized $$a$$-Weyl’s) theorem is equivalent to Weyl’s (resp., $$a$$-Weyl’s) theorem.
Reviewer: Yufeng Lu (Dalian)

##### MSC:
 47A53 (Semi-) Fredholm operators; index theories 47A10 Spectrum, resolvent 47A11 Local spectral properties of linear operators
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