Weak sequential completeness of sequence spaces (Q685938)

It is shown that a classical theorem of summability due to Schur and Hahn can be used to give a straightforward proof of a theorem of Bennett and Kalton which asserts that the \(\beta\)-dual of a monotone sequence space is weakly sequentially complete. The methods also work for vector-valued sequence spaces. Applications to Hellinger-Toeplitz Theorems are given.