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Characterizations of elements of a double dual Banach space and their canonical reproductions

Tom 104 / 1993

Vassiliki Farmaki Studia Mathematica 104 (1993), 61-74 DOI: 10.4064/sm-104-1-61-74

Streszczenie

For every element x** in the double dual of a separable Banach space X there exists the sequence of the canonical reproductions of x** in the even-order duals of X. In this paper we prove that every such sequence defines a spreading model for X. Using this result we characterize the elements of X**╲ X which belong to the class B_1 (X)╲ B_{1/2}(X) (resp. to the class B_{1/4}(X)) as the elements with the sequence (x^{(2n)}) equivalent to the usual basis of ℓ^1 (resp. as the elements with the sequence (x^{(4n-2)} - x^{(4n)}) equivalent to the usual basis of c_0). Also, by analogous conditions but of isometric nature, we characterize the embeddability of ℓ^1 (resp. c_0) in X.

Autorzy

  • Vassiliki Farmaki

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