Characterizations of elements of a double dual Banach space and their canonical reproductions
Studia Mathematica, Tome 104 (1993) no. 1, pp. 61-74
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $(x^{(2n)})$ 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.
@article{10_4064_sm_104_1_61_74,
author = {Vassiliki Farmaki},
title = {Characterizations of elements of a double dual {Banach} space and their canonical reproductions},
journal = {Studia Mathematica},
pages = {61--74},
publisher = {mathdoc},
volume = {104},
number = {1},
year = {1993},
doi = {10.4064/sm-104-1-61-74},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-104-1-61-74/}
}
TY - JOUR AU - Vassiliki Farmaki TI - Characterizations of elements of a double dual Banach space and their canonical reproductions JO - Studia Mathematica PY - 1993 SP - 61 EP - 74 VL - 104 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-104-1-61-74/ DO - 10.4064/sm-104-1-61-74 LA - en ID - 10_4064_sm_104_1_61_74 ER -
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Vassiliki Farmaki. Characterizations of elements of a double dual Banach space and their canonical reproductions. Studia Mathematica, Tome 104 (1993) no. 1, pp. 61-74. doi: 10.4064/sm-104-1-61-74
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