scholarly journals Surjectivity results for nonlinear weakly sequentially continuous operators and applications

2021 ◽  
Vol 22 (2) ◽  
pp. 481-494
Author(s):  
Afif Ben Amar ◽  
◽  
Hajer Garbout ◽  
Donal O'Regan ◽  
◽  
...  
Keyword(s):  
Weakly Sequentially Continuous ◽  
Continuous Operators

A Short Proof of Vladimirskii′s Theorem on Precompact Perturbations in Locally Convex Spaces

1975 ◽  
Vol 18 (5) ◽  
pp. 649-655
Author(s):  
Le Quang Chu
Keyword(s):  
Compact Operator ◽  
Short Proof ◽  
Locally Convex Spaces ◽  
Fréchet Spaces ◽  
Continuous Operators ◽  
Locally Convex ◽  
Convex Spaces

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.

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