Timeline for On dense embedding of Banach spaces
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2020 at 18:29 | comment | added | Jochen Wengenroth | There is a version for complete metric groups of this lemma in Tougeron's book Ideaux de Fonctions Differentiables which I can't check now because of Corona. | |
| Apr 2, 2020 at 15:41 | comment | added | Bill Johnson | "Every separable Banach space is isometrically isomorphic to a quotient of $\ell_1$." | |
| Apr 2, 2020 at 15:35 | comment | added | Bill Johnson | Probably it was when I was a graduate student when I first saw what is called the "little open mapping theorem". It says that if $T$ is in $L(X,Y)$ and the closure of $T\mathring{B}_X(1)$ contains $\mathring{B}_Y(r)$, then $T\mathring{B}_X(1)$ contains $\mathring{B}_Y(r)$. The first step is of course the proof of what you call Sandy's approximation lemma. The open mapping theorem is an immediate consequence of the LOMT. A non linear version of this was useful when I was working on Lipschitz quotient mappings $20+$ years ago. After proving the LOMT in class, an easy HW problem is... | |
| Apr 2, 2020 at 14:39 | comment | added | Nik Weaver | Aargh, switched them back. | |
| Apr 2, 2020 at 14:39 | history | edited | Nik Weaver | CC BY-SA 4.0 |
edited body
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| Apr 2, 2020 at 14:37 | comment | added | Nik Weaver | @JochenGlueck: you are welcome! | |
| Apr 2, 2020 at 14:32 | comment | added | Nik Weaver | @NateEldredge: I didn't notice that, fixed. | |
| Apr 2, 2020 at 14:30 | history | edited | Nik Weaver | CC BY-SA 4.0 |
added 1 character in body
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| Apr 2, 2020 at 14:21 | comment | added | Jochen Glueck | Ha! Thanks a lot, you just saved my day! I thought I'd loose my mind... | |
| Apr 2, 2020 at 14:19 | vote | accept | Jochen Glueck | ||
| Apr 2, 2020 at 14:12 | history | answered | Nik Weaver | CC BY-SA 4.0 |