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

More documents

Recommendations

Info

Consequences of the Hahn-Banach theorems Proof. By Theorem 3.5 there is a l ∈ X ∗ such that l(M0) = {0} and l(x0) = 1. Let x ∈ M. Then x − f (x)x0 ∈ M0 (since f (−f (x)x0) = f (x) − f (x)f (x0) = 0), and hence l(x − f (x)x0) = 0. It follows that l(x) = f (x). Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Consequences of the Hahn-Banach theorems Theorem (Theorem 3.7) Let X be a locally convex topological vector space. Let B ⊆ X be a convex, balanced and closed subset. Let x0 ∈ X \B. There is an l ∈ X ∗ such that |l(x)| ≤ 1 for all x ∈ B while l(x0) > 1. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Page 1 and 2: 7. Consequences of the Hahn-Banach
Page 3 and 4: We read in W. Rudin: Functional Ana
Page 5 and 6: Consequences of the Hahn-Banach the
Page 19: Consequences of the Hahn-Banach the
Page 27 and 28: Weak vector space topologies Let X
Page 29 and 30: Weak vector space topologies Let X
Page 31 and 32: Weak vector space topologies Lemma
Page 37 and 38: Weak vector space topologies Proof.
Page 41 and 42: Weak vector space topologies Theore
Page 71 and 72:
Weak vector space topologies Proof.
Page 73 and 74:
Page 75 and 76:
Page 77:
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?