Timeline for Regarding subspace generated by the polynomial multiples of outer functions
Current License: CC BY-SA 4.0
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| Dec 8 at 5:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Jul 31, 2020 at 20:55 | answer | added | Mateusz Kwaśnicki | timeline score: 0 | |
| Jul 31, 2020 at 19:10 | history | edited | user429197 | CC BY-SA 4.0 |
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| Jul 31, 2020 at 18:47 | comment | added | user429197 | @ChristianRemling I still have a part of the question remaining which asks if the distance is bounded below by any positive real number... | |
| Jul 31, 2020 at 18:46 | history | undeleted | user429197 | ||
| Jul 31, 2020 at 18:45 | history | deleted | user429197 | via Vote | |
| Jul 31, 2020 at 18:27 | comment | added | Christian Remling | By the way, math.stackexchange.com is a better site to ask such questions. | |
| Jul 31, 2020 at 18:25 | comment | added | Christian Remling | You have basically answered your own question already (and the answer is, yes, $1\notin P[h]$ if $h$ is not outer). This follows because $P[h]$ is invariant under multiplication by $z$, so if we had $1\in P[h]$, then this space would contain all polynomials. (And then the distance is positive automatically, as $P[h]$ is closed.) | |
| Jul 31, 2020 at 16:38 | history | edited | user429197 | CC BY-SA 4.0 |
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| Jul 31, 2020 at 13:32 | comment | added | Mateusz Kwaśnicki | The answer to (1) depends on what you mean by a "subspace generated by (...)". If you mean "closed subspace generated by (...)", as suggested by the remaining part of the quoted sentence, then yes, $\mathscr P[h]$ is closed. :-) | |
| Jul 31, 2020 at 13:17 | history | asked | user429197 | CC BY-SA 4.0 |