Timeline for Are extensions of nuclear Fréchet spaces nuclear?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2011 at 0:37 | comment | added | Ralf | Oh, my bad and a prime example of wishful reading. Thank you for the correction and the counterexample, Andrew. | |
| Apr 13, 2011 at 0:29 | vote | accept | Ralf | ||
| Apr 13, 2011 at 0:29 | |||||
| Apr 1, 2011 at 8:00 | comment | added | Andrew Stacey | Indeed, I read in the introduction to that paper "Gejler has proved that a nuclear Frechet space has the lifting property for the class of all nuclear Frechet spaces if and only if it is finite dimensional." | |
| Apr 1, 2011 at 7:34 | comment | added | Andrew Stacey | Example 3 on p96 says "Each nuclear DF -space has the lift property for the class of Frechet spaces" so it **does not apply. Indeed, here's an example of a short exact sequence of nuclear Frechet spaces that does not split: $L_\flat \mathbb{R} \to L\mathbb{R} \to \mathbb{R}^{\mathbb{N}}$. The middle is smooth loops in R and the left-hand is smooth loops that are infinitely flat at the identity. This does not split, but all are nuclear Frechet spaces. | |
| Mar 31, 2011 at 22:06 | comment | added | Yemon Choi | Glad to hear that my vague memory was correct - I wrote the comment not to be cryptic, but because I was in a rush earlier and didn't have time to chase down the references. | |
| Mar 31, 2011 at 22:03 | history | answered | Ralf | CC BY-SA 2.5 |