Timeline for Schwartz kernel theorem for topological spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 2, 2013 at 20:14 | vote | accept | AlexE | ||
| Feb 1, 2013 at 14:58 | comment | added | jbc | A suitable reference is the two volume treatise on topological vector spaces by G. Koethe. | |
| Feb 1, 2013 at 14:57 | comment | added | jbc | I thought that I had given the topology a name---that of uniform convergence on the compact subsets of $E$. Another description is as the finest locally convex topology which agrees with the weak* topology on the unit ball for tne norm on $C(K_1)'$ as the dual of $C(K_1)$, i.e., the bounded weak* topology . Indeed it is the finest toplogy (not necessarily locally convex or even linear ) which agrees with this topology on the balls. This all works in suitable form for the dual of any Banach space (even Fr\'echet space)---it is the essential content of the Banach-Dieudonn\'e theorem. | |
| Feb 1, 2013 at 11:25 | comment | added | AlexE | By "unit ball of $C(K_1)\prime$" you mean $C(K_1)\prime$ equipped with the operator norm and then the unit ball of it? And has the "natural locally convex topology on the dual of $C(K_1)$" a name, so that I can find more information about it? | |
| Feb 1, 2013 at 7:49 | comment | added | Jochen Wengenroth | The answers of jbc and Peter Michor are more or less the same as both describe the $\varepsilon$-product $C(K_1) \varepsilon C(K_2)$ of Laurent Schwartz. | |
| Jan 31, 2013 at 20:38 | history | answered | jbc | CC BY-SA 3.0 |