06.08.2013 Views

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

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Weak vector space topologies<br />

Pro<strong>of</strong>.<br />

To prove that X ∗ = X ′ , note first that every element <strong>of</strong> X ′ is<br />

continuous with respect to <strong>the</strong> X ′ -topology, proving that X ′ ⊆ X ∗ .<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

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!