Timeline for type and cotype of spaces of continuous functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2020 at 16:06 | comment | added | F. Carbon | @user131781 this is a very useful comment, thank you very much! | |
| Feb 13, 2020 at 15:56 | vote | accept | F. Carbon | ||
| Feb 13, 2020 at 15:45 | comment | added | user131781 | This is just an addendum to Dirk Werner’s definitive answer but it might add useful information: every Banach space is isometrically isomorphic to a subspace of a $C(K)$-space (even $C([0,1])$ if separable) so there is no point in examining special properties of the latter if they are inherited by subspaces. | |
| Feb 13, 2020 at 15:14 | answer | added | Dirk Werner | timeline score: 5 | |
| Feb 13, 2020 at 14:28 | comment | added | F. Carbon | @DirkWerner Thank you very much for this comment, so this means I could not find it in the books as the answer is trivial (to somebody who knows more functional analysis than I do...). If you want you could extend your comment to an answer and I will accept it. | |
| Feb 13, 2020 at 13:03 | comment | added | Dirk Werner | It is known that $C(K)$, for infinite $K$, contains a copy of $c_0$, hence it does not have nontrivial type (meaning $>1$) or nontrivial cotype (meaning $<\infty$). | |
| Feb 13, 2020 at 12:24 | history | asked | F. Carbon | CC BY-SA 4.0 |