Timeline for Finding closed subspaces whose sum isn't closed
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 12, 2023 at 14:58 | answer | added | S Argyros | timeline score: 3 | |
| Jan 6, 2023 at 14:18 | answer | added | S Argyros | timeline score: 3 | |
| Jan 5, 2023 at 10:50 | answer | added | S Argyros | timeline score: 3 | |
| Dec 29, 2022 at 16:30 | answer | added | S Argyros | timeline score: 2 | |
| Dec 28, 2022 at 16:08 | answer | added | S Argyros | timeline score: 1 | |
| Dec 24, 2022 at 16:03 | vote | accept | Nik Weaver | ||
| Dec 23, 2022 at 23:20 | answer | added | Bill Johnson | timeline score: 9 | |
| Dec 21, 2022 at 18:11 | comment | added | Nik Weaver | Hah! I didn't think of that. | |
| Dec 21, 2022 at 17:23 | comment | added | Christian Remling | By the way, ending a question title with the word "closed" can be quite confusing for a second. (At least, you didn't write "[closed]".) | |
| Dec 21, 2022 at 12:21 | comment | added | S Argyros | I mean Schauder basic sequences which by Mazur Theorem exist in any infinite dimensional Banach space. | |
| Dec 21, 2022 at 12:16 | comment | added | Nik Weaver | My thought before posting was to do this with uniformly discrete sequences, but I didn't quite see why the intersection still had to be zero. | |
| Dec 21, 2022 at 12:15 | comment | added | Nik Weaver | What is a "normalized basic sequence"? Do all Banach spaces have them? | |
| Dec 21, 2022 at 11:52 | comment | added | S Argyros | A possible approach: First find a closed subspace $W$ such that $V_0 \cap W = 0$. If their sum is not closed then we finish. Otherwise find $ ( x_n )$ in $V_0$ and $( y_n ) $ in $W$ normalized basic sequences and set $ Z $ the closed subspace generated by $ ( x_n + 2^{-n } y_n )$. Then the sum of $V_0 $ and $Z $ is not closed. | |
| Dec 21, 2022 at 4:59 | history | edited | Nik Weaver | CC BY-SA 4.0 |
added 6 characters in body
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| Dec 21, 2022 at 3:15 | history | asked | Nik Weaver | CC BY-SA 4.0 |