Timeline for Approximation property counterexamples? (Also: relation to tensor products)
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2018 at 15:57 | comment | added | Bill Johnson | Yes, that is the one, Phil. Sorry for no references; I don't have checking possibilities from where I am now. | |
| Jul 5, 2018 at 11:04 | comment | added | Philip Brooker | @YemonChoi I wasn't aware of the MAA volume either, but it would seem to be this one: books.google.com.au/books/about/… | |
| Jul 4, 2018 at 17:19 | comment | added | Yemon Choi | Thank you @BillJohnson - to be honest, I hesitated about leaving an answer when I feel I should just have resurrected the "ask-johnson" tag... I wasn't aware of Figiel's argument, but I will see if I can hunt down the MAA volume you refer to | |
| Jul 4, 2018 at 11:19 | comment | added | Jeff Egger | Thanks! This is quite helpful. I will see if I can lay my hands on a copy of Ryan's book. | |
| Jul 4, 2018 at 3:55 | comment | added | Bill Johnson | Figiel independently proved the same thing as Davie using a combinatorial rather than probabilistic argument. He did not publish it because Davie wrote up his proof quickly, but I wrote an outline of his proof as a problem set in an article in an MAA volume edited by Bartle. Szankowski is the person who proved that $\ell_p$, $1\le p < 2$, has a subspace that fails the approximation property. | |
| Jul 4, 2018 at 3:06 | comment | added | Yemon Choi | I guess this may still be somewhat unsatisfactory in the sense that one doesn't obtain explicit $X$ and $Y$ for which the comparison map between tensor products is non-injective. IIRC, the (in)famous Banach space of Pisier, which I'll call $P$, has the property that $P \overline{\otimes}_\pi P^* \to P \overline{\otimes}_{\varepsilon} P^*$ is non-injective. But this should probably wait for a proper expert to come along | |
| Jul 4, 2018 at 3:01 | history | answered | Yemon Choi | CC BY-SA 4.0 |