Asymptotic unconditionality

S. R. Cowell, N. J. Kalton

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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→∞ ∥x* + xn* = lim n→∞ ∥x*-xn*∥ 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.

Original languageEnglish
Pages (from-to)217-240
Number of pages24
JournalQuarterly Journal of Mathematics
Issue number2
Publication statusPublished - Jun 2010

ASJC Scopus subject areas

  • General Mathematics


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