An Atkinson-type theorem for B-Fredholm operators

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Generalized Weyl's theorem and hyponormal operators (2004, background): “(See [16, Proposition 6] and [12, Corollary 2.2].) In [ 6, Theorem 3.4 ] it is shown that T is a B-Fredholm operator if and only if its projection in the algebra L.X/=F0.X/ is Drazin invertible, where F0.X/ is the ideal of finite rank operators in the algebra L.X/ of bounded linear operators acting ”
Index of B-Fredholm operators and generalization of a Weyl theorem (2002, background): “(See [14, Proposition 6] and [12, Corollary 2.2].) In [ 5, Theorem 3.4 ] we have shown that a bounded linear operator T acting on a Banach space X is a B-Fredholm operator if and only if its projection in the algebraL(X)=F0(X) is Drazin invertible, whereF0(X )i s the ideal of nite rank operators in ”