CHARACTERIZATIONS OF ELEMENTS OF A DOUBLE DUAL BANACH-SPACE AND THEIRCANONICAL REPRODUCTIONS

For every element x* in the double dual of a separable Banach space X there exists the sequence (x(2n)) of the canonical reproductions of x * in the even-order duals of X. In this paper we prove that every suc h sequence defines a spreading model for X. Using this result we chara cterize the elements of X*\X which belong to the class B1(X)\B1/2(X) (resp. to the class B1/4(X)) as the elements with the sequence (x(2n)) equivalent to the usual basis of l1 (resp. as the elements with the s equence (x(4n-2)-x(4n)) equivalent to the usual basis of c0). Also, by analogous conditions but of isometric nature, we characterize the emb eddability of l1 (resp. c0) in X.