Perturbations of semi-Fredholm operators with complemented range
The author notes, for a bounded linear operator A and a compact linear operator K between Banach spaces X and Y, extending a result of \textit{J. R. Holub} [Acta Mat. Hung. 44, 269-273 (1984; Zbl 0574.47013)], that if A: \(X\to Y\) is semi-Fredholm with range R(A) complemented in Y, then the range \(R(A+K)\) of \(A+K\) is also complemented in Y. This is also true with A replaced by a closed linear operator \(A: D(A)\subset X\to Y\) and K by a relatively compact linear operator \(K: D(K)\subset X\to Y\) with respect to A.
scientific article; zbMATH DE number 4144768