On basic sequences in dual Banach spaces

A short proof of the following result is given: for every semi-normalized sequence ( x n ∗ ) in a dual Banach space X ∗ with 0 ∈ { x n ∗ } ¯ w ∗ , there exists a bounded sequence ( x n ) in X and a basic subsequence ( x k n ∗ ) such that 〈 x k i ∗ , x j 〉 = δ i j .