Timeline for Weak star separable and separable quotient problem
Current License: CC BY-SA 4.0
7 events
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| Feb 10, 2020 at 19:40 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
added 4 characters in body; edited title
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| Oct 26, 2011 at 4:27 | comment | added | Qingping Zeng | Thanks,Bill. Great "BTW". Your answer is a good application of Gowers' dichotomy. | |
| Oct 25, 2011 at 20:53 | comment | added | Bill Johnson |
In the previous comment, "If $X^∗$ is not HI" should be "If $X^∗$ has no HI subspace".
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| Oct 25, 2011 at 16:36 | comment | added | Bill Johnson |
BTW: If $X^*$ is not HI, then $X$ has a separable quotient. Indeed, then by Gowers $X^*$ contains a subspace with an unconditional basis and hence, by James, a copy of $c_0$, $\ell_1$, or an infinite dimensional reflexive space. In the last case, $X$ has a reflexive quotient. In the first case, $X$ contains a complemented subspace isomorphic to $\ell_1$ by Bessaga-Pelczynski. In the middle case, $X$ has a quotient isomorphic to either $c_0$ or $\ell_1$ by combining results of Rosenthal and mine and Hagler and mine.
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| Oct 25, 2011 at 15:06 | answer | added | Bill Johnson | timeline score: 2 | |
| Oct 25, 2011 at 13:09 | history | edited | Emil Jeřábek | CC BY-SA 3.0 |
fix markup
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| Oct 25, 2011 at 13:02 | history | asked | Qingping Zeng | CC BY-SA 3.0 |