Asymptotic Unconditionality
نویسندگان
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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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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