Timeline for $L$-decompositions of $\ell_1$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 26, 2017 at 18:42 | vote | accept | Fred Dashiell | ||
| Jan 26, 2017 at 14:10 | comment | added | user83457 | Do you mean sequences with $\sum |a_i| < \infty $ by $\ell_1$? | |
| Jan 26, 2017 at 10:31 | comment | added | anonymous | Having a decomposition such as this can be phrased as "$E$ is an L-summand in $\ell^1$". You have a corresponding continuous projection with image $E$ and kernel $F$. For further reading, I recommend this monograph: Harmand, P.; Werner, D.; Werner, W. $M$-ideals in Banach spaces and Banach algebras. Lecture Notes in Mathematics, 1547. Springer-Verlag, Berlin, 1993. viii+387 pp. ISBN: 3-540-56814-X MR1238713 | |
| Jan 26, 2017 at 9:19 | comment | added | user1688 | You have an isometric isomorphism from $E\times F$ to $\ell_1$,where $E\times F$ is equipped with the sum norm. Since $E$ and $F$ are closed in $E\times F$, they are in $\ell_1$. | |
| Jan 26, 2017 at 6:15 | answer | added | August Cleaner | timeline score: 4 | |
| Jan 26, 2017 at 5:29 | history | asked | Fred Dashiell | CC BY-SA 3.0 |