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:
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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]).
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2) The embedding of separable reflexive Banach spaces into reflexive spaces with basis (fZl).
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3) The existence of long sequences of projections and hence of locally uniformly convex norms in the duals of Asplund spaces. ([F-G])
