In the past few years, much progress have been made on several open problems in infinite dimensional Banach space theory. Here are some of the most recent results:
1) The existence of boundedly complete basic sequences in a large class of Banach spaces including the ones with the so-called Radon-Nikodym property ([G-M2], [G-M4]).
2) The embedding of separable reflexive Banach spaces into reflexive spaces with basis (fZl).
3) The existence of long sequences of projections and hence of locally uniformly convex norms in the duals of Asplund spaces. ([F-G])
