Timeline for Antiproximanal subspace of $L_1[0,1]$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2016 at 22:32 | vote | accept | Norbert | ||
| Jan 13, 2016 at 22:13 | answer | added | Bill Johnson | timeline score: 2 | |
| Jan 13, 2016 at 21:22 | comment | added | Norbert | @BillJohnson, why don't you post this as answer? | |
| Jan 13, 2016 at 16:25 | comment | added | Bill Johnson | The $Y$ in Mikhail's answer has codimension one. Obviously $Y$ cannot be reflexive, but $Y$ can be of any non zero finite codimension or of infinite codimension. (Let $Z$ be any separable Banach space and let $Q$ be an operator from $L_1$ to $Z$ that maps the closed unit ball of $L_1$ onto the open unit ball of $Z$. The kernel $Y$ of such a quotient map $Q$ is antiproximinal. It is easy to built such an operator from $\ell_1$ onto $Z$; to get one from $L_1$ compose the operator from $\ell_1$ with a norm one projection from $L_1$ onto a subspace that is isometric to $\ell_1$.) | |
| Jan 13, 2016 at 11:02 | vote | accept | Norbert | ||
| Jan 13, 2016 at 22:32 | |||||
| Jan 13, 2016 at 5:25 | answer | added | Mikhail Ostrovskii | timeline score: 6 | |
| Jan 12, 2016 at 23:58 | history | asked | Norbert | CC BY-SA 3.0 |