Timeline for Subspaces of $l_{1}$ are not Lipschitz complemented in $l_{1}$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2014 at 2:18 | comment | added | François G. Dorais | Dear Dongyang Chen, please follow this link - mathoverflow.net/contact - to arrange for your two accounts to be merged: #41619 #54727. | |
| Jul 6, 2014 at 22:08 | comment | added | Yemon Choi | @BillJohnson Thanks - I knew I was missunderstanding something basic | |
| Jul 6, 2014 at 21:38 | comment | added | Bill Johnson | @Yemon Choi: A Lipschitz right inverse to the quotient gives a Lipschitz projection, but the converse is false. for example, $C[0,1]$ is Lipschitz complemented in every superspace by Lindenstrauss' 1964 paper, but, as you know, it is not complemented in every separable superspace; in particular the functions that are right continuous, left continuous except at the rationals, and have left limits at the rationals. | |
| Jul 6, 2014 at 19:37 | answer | added | Tony Prochazka | timeline score: 1 | |
| Jul 6, 2014 at 19:28 | comment | added | Yemon Choi | @BillJohnson I must be missing something -- isn't this handled by Godefroy--Kalton? (If there were a Lipschitz complementation, then surely there'd be a Lipschitz right inverse to the quotient map, hence a bounded linear right inverse by the GK results; and we know that $L_1[0,1]$ is not isomorphic to any complemented subspace of $\ell_1$... | |
| Jul 6, 2014 at 18:02 | comment | added | Bill Johnson | The question is very interesting IMO. | |
| Jul 6, 2014 at 18:00 | history | edited | Bill Johnson |
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| Jul 6, 2014 at 16:58 | review | First posts | |||
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| Jul 6, 2014 at 16:41 | history | asked | Dongyang Chen | CC BY-SA 3.0 |