Timeline for ED compact $K$ such that $C(K)$ is not a dual Banach space
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 31, 2015 at 18:06 | comment | added | Tristan Bice | I also had trouble tracking down this paper a while back. As Choi mentions, the counter-example consists of bounded Borel functions modulo those with meagre support. I guessed at the proof (basically as outlined in the book mentioned by Dashiell it seems) and posted it in answer to another question here - math.stackexchange.com/questions/856804/…. | |
| Feb 27, 2015 at 17:21 | comment | added | Dmitri Pavlov | Dixmier's paper is available here: dmitripavlov.org/scans/dixmier.pdf | |
| Jan 12, 2012 at 6:51 | vote | accept | TomK | ||
| Jan 9, 2012 at 9:48 | comment | added | Philip Brooker | Further to my earlier comment concerning Rosenthal's paper, see Section 4 of that paper (i.e., Section 4 of On injective banach spaces and the spaces $L_\infty(\mu)$ for finite measures $\mu$, Acta Math. **124**(1) (1970), 205-248). There it is discussed how work of Haim Gaifman yields a stonean compact $K$ such that $C(K)$ is not a dual space. I think the relevant papers are quite easily accessible. | |
| Jan 8, 2012 at 6:41 | comment | added | Philip Brooker | Just a quick comment, based on a rather hazy memory (I may expand on it when I have more time and can check for myself): look inside Haskell Rosenthal's Acta Mathematica paper on injective Banach spaces (late 1960s?) for an injective $C(K)$ space that is not a dual space; I believe that such a space is discussed there... maybe the $K$ there is extremally disconnected? | |
| Jan 7, 2012 at 2:27 | answer | added | Fred Dashiell | timeline score: 3 | |
| Jan 7, 2012 at 1:01 | comment | added | Gerald Edgar | extremely disconnected -> extremally disconnected ?? | |
| Jan 6, 2012 at 23:13 | answer | added | Yemon Choi | timeline score: 3 | |
| Jan 6, 2012 at 22:38 | history | edited | TomK | CC BY-SA 3.0 |
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| Jan 6, 2012 at 22:24 | history | asked | TomK | CC BY-SA 3.0 |