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

• Autorzy: Vassiliki Farmaki
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 1
• Strony: 61-74

Daty

wydano

1993

otrzymano

1991-10-01

poprawiono

1992-08-05

Twórcy

autor

Vassiliki Farmaki

• Department of Mathematics, University of Athens, Panepistemiopolis-Ilisia, Gr-15784 Athens, Greece ,

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