Timeline for Grothendieck on topological vector spaces
Current License: CC BY-SA 4.0
26 events
| when toggle format | what | by | license | comment | |
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| Apr 9 at 15:15 | history | edited | The Amplitwist | CC BY-SA 4.0 |
HTTP -> HTTPS (thread was bumped by a new answer)
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| Apr 9 at 14:36 | history | edited | YCor | CC BY-SA 4.0 |
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| Apr 9 at 14:31 | answer | added | user234212323 | timeline score: 2 | |
| Nov 19, 2017 at 19:11 | answer | added | Abdelmalek Abdesselam | timeline score: 3 | |
| Sep 28, 2014 at 15:05 | comment | added | Sergei Akbarov | I forgot the category of convenient spaces: ncatlab.org/nlab/show/convenient+vector+space. It seems to me it possesses some of these properties (without auto-duality, as far as I know). @PeterMichor can clarify this. | |
| Sep 28, 2014 at 14:47 | comment | added | Sergei Akbarov | As to $\ell_1$, this is a question of habits. What we see every day becomes our own, like our relatives or friends. | |
| Sep 28, 2014 at 14:34 | comment | added | Sergei Akbarov | Yemon, no, it isn't. Because this duality generates a closed monoidal category ${\tt Ste}$ of stereotype spaces, the second one in Analysis after the category ${\tt Ban}$ of Banach spaces with this property, and this auto-duality (with many other remarkable properties) makes ${\tt Ste}$ better than ${\tt Ban}$. IMHO. :) | |
| Sep 28, 2014 at 13:35 | answer | added | Anatoly Kochubei | timeline score: 5 | |
| Sep 28, 2014 at 12:52 | comment | added | Yemon Choi | Furthermore, the fact that the bidual-in-usual sense of the Banach algebra $\ell_1({\bf N})$ is naturally related to $\beta{\bf N}$ makes me less inclined to work with adjoint functors which make the canonical map of a Banach space to its "bidual" an isomorphism | |
| Sep 28, 2014 at 12:48 | comment | added | Yemon Choi | @SergeiAkbarov I don't wish to start a long, drawn-out debate in the comments, and I'm sure you have read more about TVS than I have, but isn't the self-biduality you mention some kind of Mackey duality? | |
| Sep 28, 2014 at 12:47 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Sep 28, 2014 at 12:30 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
retagged question; edited body
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| Sep 28, 2014 at 7:34 | comment | added | Sergei Akbarov | As an illustration: who knows that every Banach space $X$ becomes relexive, $X^{\star\star}=X$, if we endow its dual space $X^\star$ with the compact-open topology? This was found in 1952 by Marianne Smith. When I am telling this to people they are surprised. Formally this is absurd: the simple explanation is less known than the intricate one. A reference for those who find this unexpected: en.wikipedia.org/wiki/Stereotype_space. | |
| Sep 28, 2014 at 6:51 | comment | added | Sergei Akbarov | I upvoted Yemon's comment, but this was a mistake. In my opinion, the theory of TVS is indeed dead, and the most part of the guilt for this lies on Alexander Grothedieck. It must have been evident from the very beginning that there is something wrong in this abundance of topologies on the dual space, duality theories, counter-examples, etc. After its birth the theory immediately turned into a long list of counterexamples. The scientific explanation can't be so intricate, knotty, this is an abuse of professional knowledge. | |
| Sep 28, 2014 at 5:59 | answer | added | asv | timeline score: 4 | |
| Dec 19, 2012 at 10:46 | answer | added | Alexei Pirkovskii | timeline score: 24 | |
| Mar 18, 2012 at 14:33 | answer | added | Ronnie Brown | timeline score: 20 | |
| Mar 11, 2012 at 8:39 | history | edited | Uday | CC BY-SA 3.0 |
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| Mar 11, 2012 at 8:35 | comment | added | Uday | @Yemon Thank you for sensitizing. I have removed the question. Rephrased the original question. | |
| Mar 11, 2012 at 8:32 | history | edited | Uday | CC BY-SA 3.0 |
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| Mar 11, 2012 at 8:06 | comment | added | Yemon Choi | I would prefer it if you replaced "Is TVS really dead?" with a more well-defined, and less subjective, question. | |
| Mar 11, 2012 at 2:34 | answer | added | Mozibur Ullah | timeline score: 6 | |
| Mar 10, 2012 at 21:52 | answer | added | Charles Matthews | timeline score: 11 | |
| Mar 10, 2012 at 20:33 | history | edited | Uday | CC BY-SA 3.0 |
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| Mar 10, 2012 at 19:13 | comment | added | Martin Brandenburg | At least there are still papers on that subject. But Grothendieck would certainly pay no attention to them and hang on his statement from the 60s ;). | |
| Mar 10, 2012 at 18:28 | history | asked | Uday | CC BY-SA 3.0 |