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

Farmaki, Vassiliki

Studia Mathematica, Tome 104 (1993), p. 61-74 / Harvested from The Polish Digital Mathematics Library

Résumé

For every element x** in the double dual of a separable Banach space X there exists the sequence $(x^{(2 n)})$ 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 $(x^{(2 n)})$ equivalent to the usual basis of $ℓ^{1}$ (resp. as the elements with the sequence $(x^{(4 n - 2)} - x^{(4 n)})$ 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.

Publié le : 1993-01-01

Zbl 0814.46014

EUDML-ID : urn:eudml:doc:215959

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     author = {Vassiliki Farmaki},
     title = {Characterizations of elements of a double dual Banach space and their canonical reproductions},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {61-74},
     zbl = {0814.46014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i1p61bwm}
}

Farmaki, Vassiliki. Characterizations of elements of a double dual Banach space and their canonical reproductions. Studia Mathematica, Tome 104 (1993) pp. 61-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i1p61bwm/

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