ASYMPTOTIC UNCONDITIONALITY

作者：Cowell S R; Kalton N J^*

来源：The Quarterly Journal of Mathematics, 2010, 61(2): 217-240.

DOI：10.1093/qmath/han036

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 ->infinity) parallel to x* x(n)*parallel to = lim(n ->infinity) parallel to x* - x(n)*parallel to whenever x* is an element of X*, (x(n)*)(n=1)(infinity) 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.

• 出版日期2010-6