Covering dimension and nonlinear equations

Details Covering dimension and nonlinear equations Covering dimension and nonlinear equations

2004-12-31

arxiv.org/abs/math/0412563v1

RIMS Kokyuroku 1031, 97-100 (1998)

Mathematics

Functional Analysis

3 pages

Scientific paper

Theorem: Let X and Y be two Banach spaces, Phi: X to Y a continuous, linear,
surjective operator, and Psi: X to Y a completely continuous operator with
bounded range. Then, one has dim{x in X : Phi(x)=Psi(x)} >= dim(Phi^{-1}(0)).
Here dim denotes the covering dimension.

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