Timeline for Analogues of properties (DN) and (Ω) for more general locally convex spaces
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| Sep 17, 2017 at 0:18 | comment | added | David Roberts♦ | @Jochen I was wondering about any extensions of splitting theorems past the Fréchet setting, and curious to know how badly things can go wrong when just taking a naïve approach. But also for its own sake. The test case I have in mind is compactly-supported smooth functions. For those following, here's a pdf of the Bonet-Domanski paper jbonet.webs.upv.es/wp-content/uploads/papers/2008/… - thanks for the reference. | |
| Sep 16, 2017 at 14:33 | comment | added | Jochen Wengenroth | What do you want to do with such generalizations? If you are looking for splitting results: It is known e.g. that every short exact sequence $0\to E\to F\to G\to 0$ splits if $E$ is a quotient of the spaces of distribution $\scr D'$, $G$ is a subspace of $\scr D'$ and $F$ is a PLS-space. | |
| Sep 16, 2017 at 14:27 | comment | added | Jochen Wengenroth | There are splitting results for so-called PLB-spaces (countable projective limits of countable inductive limits of Banach spaces) by Bonet and Domanski where generalizations of DN for those spaces (called "dual interpolation estimates") play an important role. Look at the article ''The splitting of short exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations'', Advances in Mathematics 217, no. 2, (2008) 561-585 | |
| Sep 16, 2017 at 8:29 | history | asked | David Roberts♦ | CC BY-SA 3.0 |