Let $X$ be a space and $Q_{X}:X^{**}\rightarrow X^{**}/X$ be the canonical quotient map. Given a weakly null sequence $(f_{n})_{n}$ in $X^{**}/X$. Is there a weakly Cauchy sequence $(x^{**}_{n})_{n}$ in $X^{**}$ such that $Q_{X}(x^{**}_{n})=f_{n}$ for all $n$? If it is false, how about for a space $X$ containing no copy of $l_{1}$?
$\begingroup$
$\endgroup$
1
asked Oct 21, 2015 at 16:23
-
$\begingroup$ Should I interpret your first sentence to be "Let $X$ be a locally convex topological vector space"? $\endgroup$– André HenriquesCommented Oct 21, 2015 at 18:46
Add a comment
|