Timeline for Which Fréchet spaces have a dual that is a Fréchet space?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2012 at 15:42 | comment | added | Tobias Diez | @Andrew Stacey: Where can one find a proof and detailed discussion of your statement? Thanks! | |
| Apr 29, 2011 at 8:55 | comment | added | Andrey Rekalo | @Andrew Stacey: That's really nice and intuitively appealing. | |
| Apr 29, 2011 at 8:45 | comment | added | Andrew Stacey | A nice way to think of this is as the observation that a LCTVS cannot be a (non-trivial) projective limit and an inductive limit of countably infinite families of Banach spaces at the same time. Either one family has to be uncountable, or both have to be finite. | |
| Apr 29, 2011 at 8:02 | comment | added | Andrey Rekalo | @David Roberts: This implies that the claim stated by the OP holds true. The observation is probably due to Grothendieck. | |
| Apr 29, 2011 at 7:56 | comment | added | David Roberts♦ | SO what does this mean for the question, for someone who doesn't have instant recall about the lattice of properties of topological vector spaces? | |
| Apr 29, 2011 at 7:53 | vote | accept | Tim van Beek | ||
| Apr 29, 2011 at 7:52 | comment | added | Tim van Beek | Thanks, so one has to combine §21.5 (3): "For a Fréchet space, the original topology is equal to the strong topology", with §29.1 (7), which is what you quoted. | |
| Apr 29, 2011 at 7:34 | history | answered | Andrey Rekalo | CC BY-SA 3.0 |