7. Consequences of the Hahn-Banach theorems - Aarhus Universitet

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Consequences of the Hahn-Banach theorems Theorem (Theorem 3.6) Let X be a locally convex topological vector space and M ⊆ X a subspace. If f : M → Φ is a continuous linear functional on M, there is an l ∈ X ∗ such that l|M = f . Proof. We may assume that f is not identically 0. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Consequences of the Hahn-Banach theorems Theorem (Theorem 3.6) Let X be a locally convex topological vector space and M ⊆ X a subspace. If f : M → Φ is a continuous linear functional on M, there is an l ∈ X ∗ such that l|M = f . Proof. We may assume that f is not identically 0. Set M0 = {x ∈ M : f (x) = 0}. and choose x0 ∈ M such that f (x0) = 1. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
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7. Consequences of the Hahn-Banach theorems - Aarhus Universitet

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