2008/09/12 by Simon Cowell, S. R. Cowell, Cowell, S. R. +2
Engineering · Mathematics · #Stability and Control of Uncertain Systems #math.FA #msc:46B03 #msc:46B20
paper · pdf · doi:10.48550/arxiv.0809.2294
26 pages. Submitted for publication. This is a replacement submission. The paper is unchanged but the "Comments" field has been edited
arxiv created 2008/09/17 · arxiv updated 2009/12/01
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^* + xn^*‖ = limn → ∞ ‖x^* - xn^*‖ whenever x^* ∈ X^*, (xn^*) 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.