Timeline for Definition question: asymptotic-$\ell_{p}$ versus coordinate-free asymptotic-$\ell_{p}$
Current License: CC BY-SA 4.0
5 events
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| Mar 26, 2021 at 2:06 | comment | added | JWP_HTX | Actually, I think I have answered my own questions. The correct coordinate-free notion above glosses over how the subspaces of finite codimension are chosen (i.e. as part of a 2-player game like in Remark 3.8 of this paper by Argyros and Motakis). I would, however, still be interested in examples other than $\ell_{1}(\Gamma)$ of non-separable Asymptotic-$\ell_{1}$ spaces if you happen to know of any. | |
| Mar 25, 2021 at 19:50 | comment | added | JWP_HTX | I certainly agree now that the subspaces $Y_{i}$ must have finite codimension, but I have some related questions. (1) How should I choose the subspaces (tail spaces?) in the first definition so that it also satisfies the correct coordinate-free definition? This is not obvious to me. (2) I suspect that $\ell_{1}(\Gamma)$ for $\Gamma$ uncountable satisfies the coordinate-free definition of being Asymptotic-$\ell_{1}$, but I am having some trouble proving this - is it true? If not, is there a canonical example of a non-separable Asymptotic-$\ell_{1}$ space? | |
| Sep 30, 2020 at 21:28 | comment | added | JWP_HTX | Thank you for your helpful answer! | |
| Sep 30, 2020 at 21:19 | vote | accept | JWP_HTX | ||
| Sep 30, 2020 at 20:37 | history | answered | Bunyamin Sari | CC BY-SA 4.0 |