Geodesic
Operators with Closed Range, Pseudo-Inverses, and Perturbation of Frames for a Subspace
Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 37-45

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DOI

Recent work of Ding and Huang shows that if we perturb a bounded operator (between Hilbert spaces) which has closed range, then the perturbed operator again has closed range. We extend this result by introducing a weaker perturbation condition, and our result is then used to prove a theorem about the stability of frames for a subspace.
DOI : 10.4153/CMB-1999-004-5
Mots-clés : 42C15 
Christensen, Ole. Operators with Closed Range, Pseudo-Inverses, and Perturbation of Frames for a Subspace. Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 37-45. doi: 10.4153/CMB-1999-004-5
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     title = {Operators with {Closed} {Range,} {Pseudo-Inverses,} and {Perturbation} of {Frames} for a {Subspace}},
     journal = {Canadian mathematical bulletin},
     pages = {37--45},
     year = {1999},
     volume = {42},
     number = {1},
     doi = {10.4153/CMB-1999-004-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-004-5/}
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