C-convexity in Infinite-dimensional Banach Spaces and Applications to Kergin Interpolation
نویسنده
چکیده
We investigate the concepts of linear convexity and C-convexity in complex Banach spaces. The main result is that any C-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a C-convex domain Ω in the Banach space X and a point p / ∈Ω, there is a complex hyperplane through p that does not intersect Ω. We also prove that linearly convex domains are holomorphically convex, and that Kergin interpolation can be performed on holomorphic mappings defined in C-convex domains.
منابع مشابه
ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation
We investigate the concepts of linear convexity and C-convexity in complex Banach spaces. The main result is that any C-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a C-convex domain Ω in the Banach space X and a point p / ∈Ω, there is a complex hyperplane through p that does not intersect Ω. We also prov...
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