ar X iv : 0 80 9 . 22 94 v 1 [ m at h . FA ] 1 2 Se p 20 08 ASYMPTOTIC UNCONDITIONALITY
نویسنده
چکیده
We show that a separable real Banach space embeds almost isometrically in a space Y with a shrinking 1-unconditional basis if and only if limn→∞ ‖x ∗ + x∗ n ‖ = limn→∞ ‖x ∗ − x∗ n ‖ whenever x∗ ∈ X∗, (x∗ n )∞ n=1 is a weak∗-null sequence and both limits exist. If X is reflexive then Y can be assumed reflexive. These results provide the isometric counterparts of recent work of Johnson and Zheng.
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تاریخ انتشار 2008