Timeline for A criterion for norming sets
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2017 at 20:15 | comment | added | erz | @AugustCleaner I was not able to understand it, after applying some efforts, and so decided leave this thing aside for a while | |
| Nov 19, 2017 at 18:52 | comment | added | August Cleaner | @erz Why do not you accept the answer? | |
| Aug 24, 2017 at 4:44 | comment | added | Mikhail Ostrovskii | As for $\{f_n\}$ it will suffice to approximate $f_n$, say, up to $1/n$ in $||\cdot||$, the new norm is only smaller. As for estimate of the norm of $t_k$, one can show that up to some constant $|||t_k|||$ and $||t_k||$ are equivalent. All this is standard techniques, which is developed in, for example, Lindenstrauss-Tzafriri, Classical Banach spaces, volume 1. Writing this in detail should take a rather nontrivial amount of time. | |
| Aug 23, 2017 at 10:49 | comment | added | erz | I am sorry, but could you please elaborate on the second part of the answer? Namely, why can we approximate $\{f_{k}\}$ in the way that you suggest (and it has to be with respect to $|||\cdot|||$, right?), and also the very last claim about the convergence of $|||t_k|||$? | |
| Aug 22, 2017 at 8:20 | history | answered | Mikhail Ostrovskii | CC BY-SA 3.0 |