Perturbations of semi-Fredholm operators with complemented range
type: Item
instance of: scholarly article
title: Perturbations of semi-Fredholm operators with complemented range
zbMATH Open document ID: 0698.47012
DOI: 10.1007/BF01952045
author: Seymour Goldberg
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: 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.
reviewed by: Takashi Ichinose
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 4144768
zbMATH Keywords: semi-Fredholm operator
zbMATH Keywords: complemented or complementary subspaces
zbMATH Keywords: relatively compact linear operator
MaRDI profile type: Publication
cites work: Q5784673
cites work: Q5526484
cites work: On perturbation of operators with complemented range
cites work: On the stability of the index of unbounded linear transformations
description: scientific article; zbMATH DE number 4144768