Timeline for Differentiation of a norm
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 11, 2023 at 23:28 | comment | added | Pietro Majer | Indeed, it is disontinuous everywhere, wrto the $L^\infty$ topology. | |
| Dec 11, 2023 at 13:34 | comment | added | elmas | @PietroMajer You are correct; this is what I wanted to understand. As you mentioned, the map is not even continuous in the general case. | |
| Dec 11, 2023 at 13:26 | vote | accept | elmas | ||
| Dec 10, 2023 at 17:57 | comment | added | Pietro Majer | I don’t know… maybe the question was: prove that it is differentiable at u in the domain of F if u is also in $L^2$ etc (then I guess the answer would be no, it is not even continuous wrto the $L^\infty$ topology) | |
| Dec 10, 2023 at 16:33 | comment | added | Iosif Pinelis | @PietroMajer : Thank you for your comments. Concerning your first comment: If a function $F$ takes an infinite value at some point $u$ (and also at some point in every neighborhood of $u$), how would we define a derivative of $F$ at $u$? I think we would then have to deal with something like $\infty-\infty$. | |
| Dec 10, 2023 at 15:43 | comment | added | Pietro Majer | I like so much the conclusion | |
| Dec 10, 2023 at 15:42 | comment | added | Pietro Majer | Maybe the OP means $\overline{\mathbb R}$ as a codomain of $F$… ? the whole question is unclear | |
| Dec 10, 2023 at 15:16 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |