7. Consequences of the Hahn-Banach theorems - Aarhus Universitet
7. Consequences of the Hahn-Banach theorems - Aarhus Universitet
7. Consequences of the Hahn-Banach theorems - Aarhus Universitet
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<strong>Consequences</strong> <strong>of</strong> <strong>the</strong> <strong>Hahn</strong>-<strong>Banach</strong> <strong>the</strong>orems<br />
Theorem<br />
(Theorem 3.7) Let X be a locally convex topological vector space.<br />
Let B ⊆ X be a convex, balanced and closed subset. Let<br />
x0 ∈ X \B. There is an l ∈ X ∗ such that |l(x)| ≤ 1 for all x ∈ B<br />
while l(x0) > 1.<br />
Klaus Thomsen <strong>7.</strong> <strong>Consequences</strong> <strong>of</strong> <strong>the</strong> <strong>Hahn</strong>-<strong>Banach</strong> <strong>the</strong>orems