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 />
Pro<strong>of</strong>.<br />
By Theorem 3.5 <strong>the</strong>re is a l ∈ X ∗ such that l(M0) = {0} and<br />
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