Timeline for What's an example of a space that needs the Hahn-Banach Theorem?
Current License: CC BY-SA 2.5
12 events
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| Nov 17, 2021 at 12:39 | comment | added | Abdelmalek Abdesselam | Speaking about $\ell^{\infty}$, I haven't seen any evidence in this post that "it does need the Hahn-Banach" theorem. For one, it is an abstract thing, and it sound weird to say that has needs. The question rather should be: does a mathematician need to use the Hahn-Banach Theorem (or axiom here), in order to produce a continuous linear form outside $\ell^1$. I have never felt this need, but others could perhaps inform me about why they need such a thing. | |
| Oct 15, 2021 at 21:29 | history | edited | Martin Sleziak |
added (hahn-banach-theorem)
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| Nov 20, 2009 at 19:03 | comment | added | Mark Meckes | There are other classes of Banach spaces (e.g., uniformly convex spaces) for which Hahn-Banach can also be proved constructively. As it happens, $\ell^\infty$ is one of the first non-examples to come to mind for those other classes as well. So although it's certainly not "the" answer, it's a pretty good one from many points of view. | |
| Nov 17, 2009 at 14:38 | history | edited | Andrew Stacey | CC BY-SA 2.5 |
added 520 characters in body
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| Nov 14, 2009 at 20:17 | answer | added | Gerald Edgar | timeline score: 33 | |
| Nov 14, 2009 at 5:20 | answer | added | Greg Kuperberg | timeline score: 50 | |
| Nov 14, 2009 at 1:49 | answer | added | Peter Schmitt | timeline score: -3 | |
| Nov 13, 2009 at 18:41 | answer | added | Dave Penneys | timeline score: 17 | |
| Nov 13, 2009 at 17:46 | answer | added | Ari Shnidman | timeline score: 3 | |
| Nov 13, 2009 at 15:25 | answer | added | Danny Calegari | timeline score: 13 | |
| Nov 13, 2009 at 15:08 | answer | added | Mark Meckes | timeline score: 24 | |
| Nov 13, 2009 at 14:36 | history | asked | Andrew Stacey | CC BY-SA 2.5 |