Timeline for A hyperplane separation question
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2019 at 14:32 | vote | accept | Tom Goodwillie | ||
| Oct 24, 2019 at 6:43 | answer | added | Jochen Glueck | timeline score: 5 | |
| Oct 24, 2019 at 5:52 | comment | added | Jochen Glueck | The answer is certainly yes if $K$ consists of positive functionals $\varphi$ only (where positive means that $\langle \varphi, f \rangle \ge 0$ for each $f\ge 0$). For more general $K$ I have severe doubts whether this is true, but I also couldn't find a counterexample yet. | |
| Oct 24, 2019 at 2:17 | comment | added | Tom Goodwillie | I know that for every finite set $S\subset K$ there exists $x$ such that for all $k\in S$ $k(x)>0$. | |
| Oct 24, 2019 at 1:07 | comment | added | Gerald Edgar | "Convex hull does not contain the origin". Actually, you need more: the weak* closure of the convex hull does not contain the origin. "$K$ is compact" Actually you need less: $K$ is bounded, consequently, the weak* closure of the convex hull of $K$ is weak* compact. | |
| Oct 24, 2019 at 1:07 | comment | added | Nik Weaver | Now that I see the subtlety in the question ($K$ is compact but we don't know its convex hull is compact) I'm going to delete my answer. I suspect the answer is no, but I have to think. | |
| Oct 24, 2019 at 0:44 | history | asked | Tom Goodwillie | CC BY-SA 4.0 |