From: BrendaSueCook (brenda@math.missouri.edu)
Date: Fri Mar 27 2009 - 14:34:03 CDT
Ph.D. DEFENSE
Department of Mathematics
Simon Cowell
(MU, Math)
Asymptotic Unconditionality in Banach Spaces
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
$x^*\in X^*$, $(x_n^*)_{n=1}^{\infty}$ 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.
Wednesday, April 1
10:00 a.m.
312 Math Sciences
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