We show that if E is a complex Banach space which contains no subspace isomorphic to l1, then each infinite dimensional subspace of E′ contains a normalized sequence which converges to zero for the weak star topology.
Dedicated to the memory of Klaus Floret (1941–2002).
"Banach spaces not containing l1." Ark. Mat. 41 (2) 363 - 374, October 2003. https://doi.org/10.1007/BF02390820