Asymptotic Unconditionality
S. R. Cowell, N. J. Kalton

TL;DR
This paper characterizes when a separable real Banach space can be embedded almost isometrically into a space with a shrinking 1-unconditional basis, linking geometric properties to weak*-null sequences.
Contribution
It provides a new characterization of embeddings into spaces with shrinking 1-unconditional bases using asymptotic unconditionality conditions.
Findings
Characterization of embeddings via limits involving weak*-null sequences
Extension to reflexive spaces with reflexive embeddings
Connection to recent work of Johnson and Zheng
Abstract
We show that a separable real Banach space embeds almost isometrically in a space with a shrinking 1-unconditional basis if and only if whenever , is a weak-null sequence and both limits exist. If is reflexive then can be assumed reflexive. These results provide the isometric counterparts of recent work of Johnson and Zheng.
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Taxonomy
TopicsStability and Control of Uncertain Systems
