Timeline for In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?
Current License: CC BY-SA 4.0
13 events
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| Jul 26, 2020 at 4:34 | vote | accept | Nikhil Sahoo | ||
| Jul 25, 2020 at 23:24 | answer | added | Bill Johnson | timeline score: 10 | |
| Jul 24, 2020 at 9:03 | history | edited | Jochen Wengenroth |
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| Jul 24, 2020 at 7:13 | history | became hot network question | |||
| Jul 24, 2020 at 6:26 | vote | accept | Nikhil Sahoo | ||
| Jul 26, 2020 at 4:34 | |||||
| Jul 24, 2020 at 6:25 | history | edited | Nikhil Sahoo | CC BY-SA 4.0 |
added 126 characters in body
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| Jul 24, 2020 at 5:52 | answer | added | Mikhail Ostrovskii | timeline score: 10 | |
| Jul 23, 2020 at 23:30 | comment | added | Christian Remling | What seems to work though in this case is something like $x_n=\chi_{[n,\infty)}$ (this is similar in spirit to your second example). | |
| Jul 23, 2020 at 22:45 | comment | added | Christian Remling | $e_n$ is not a $P$ sequence as a sequence from $\ell^{\infty}$ (take $y=(0,-1,0,-1,\ldots)$). | |
| Jul 23, 2020 at 20:48 | comment | added | Nikhil Sahoo | Awesome! Thanks so much. | |
| Jul 23, 2020 at 20:47 | comment | added | LSpice |
This is a nice question! I hope you don't mind that I highlighted the question itself, and added the requirement of infinite dimensionality, which it seemed to me from context to be very likely that you meant to impose. (Also, I noticed that you ran into spacing issues with $||g - \chi_p||_\infty$ ||g - \chi_p||_\infty, which you addressed with $||g - \chi_p{||}_\infty$ ||g - \chi_p{||}_\infty. Spacing and semantics can be achieved with $\|g - \chi_p\|_\infty$ \|g - \chi_p\|_\infty or, for maximal explicitness, $\lVert g - \chi_p\rVert_\infty$ \lVert g - \chi_p\rVert_\infty.)
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| Jul 23, 2020 at 20:46 | history | edited | LSpice | CC BY-SA 4.0 |
Highlighted question; required infinite dimensionality
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| Jul 23, 2020 at 20:30 | history | asked | Nikhil Sahoo | CC BY-SA 4.0 |