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arXiv · 0809.2294

Asymptotic Unconditionality

S. R. Cowell·N. J. Kalton
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Abstract

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 $\lim_{n \to \infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^* \in X^*$, $(x_n^*)$ 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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S. R. Cowell, N. J. Kalton. 2008-09-17. Asymptotic Unconditionality. https://arxiv.org/abs/0809.2294

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