Abstract
LetX be a (not necessarily closed) subspace of the dual spaceB * of a separable Banach spaceB. LetX 1 denote the set of all weak * limits of sequences inX. DefineX a , for every ordinal numbera, by the inductive rule:X a = (U b < a X b ) 1 .There is always a countable ordinala such thatX a is the weak * closure ofX; the first sucha is called theorder ofX inB * .
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