Geodesic
A Short Proof of Vladimirskii′s Theorem on Precompact Perturbations in Locally Convex Spaces
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 649-655

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Let T, P denote two continuous operators from E into F, where E and F are locally convex spaces. It is proved by L. Schwartz [8] and G. KÖthe [6] that if E and F are Fréchet spaces, T is a φ_-operator and P a compact operator, then T+P is a φ_-operator. 
Chu, Le Quang. A Short Proof of Vladimirskii′s Theorem on Precompact Perturbations in Locally Convex Spaces. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 649-655. doi: 10.4153/CMB-1975-114-5
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     author = {Chu, Le Quang},
     title = {A {Short} {Proof} of {Vladimirskii's} {Theorem} on {Precompact} {Perturbations} in {Locally} {Convex} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {649--655},
     year = {1975},
     volume = {18},
     number = {5},
     doi = {10.4153/CMB-1975-114-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-114-5/}
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