Timeline for weak*-closed subspaces

6 events

when toggle format	what		by	license	comment
Mar 7, 2012 at 21:24	comment	added	Bill Johnson		Right, Yemon: If X is complemented in any dual space, then it is complemented in its bidual.
Mar 7, 2012 at 2:58	comment	added	Yemon Choi		In fact, we don't even need the assumption that $X$ is complemented in its second dual.
Mar 7, 2012 at 2:57	comment	added	Yemon Choi		As an aside, this would seem to show that one can relax the hypotheses that $X$ is a dual space and $Y$ a weakly complemented, weak-star closed subspace to: $X$ is complemented in its second dual, $Y\subseteq X$ is complemented in its second dual, and $Y^{}$ is complemented in $X^{}$. (This might be of interest when $X$ is, for instance, the predual of a von Neumann algebra.)
Mar 7, 2012 at 2:54	vote	accept	Denis Poulin
Mar 7, 2012 at 2:28	comment	added	Denis Poulin		Dear Professor Johnson, that is a nice observation. Thank you.
Mar 7, 2012 at 2:01	history	answered	Bill Johnson	CC BY-SA 3.0