Timeline for Weak* continuity of positive parts, again
Current License: CC BY-SA 3.0
4 events
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| Dec 3, 2016 at 5:25 | comment | added | Cameron Zwarich | For Saks Spaces, the only good book I am aware of is J.B. Cooper's Saks Spaces and Applications to Functional Analysis. To wax philosophically, since all compatible dual topologies have the same continuous linear functions, the Mackey topology allows you to maximize the continuity of nonlinear functions. In many ordered spaces it has nice order properties, but I'm not aware of a single theorem that explains this. I have unfinished notes on some of this material. If I ever finish them, I'll send you a link. | |
| Dec 3, 2016 at 5:16 | comment | added | Cameron Zwarich | @UriBader Sorry for the late reply. I think most of this follows from general TVS theory and the mentioned theorems, although books on the subject often don't work out the consequences for duals of Banach spaces in detail. The bounded weak$^*$ topology is called the equicontinuous weak$^*$ topology for general TVSs, and is the least locally convex topology agreeing with the weak$^*$ topology on equicontinuous sets. In the dual of a Banach space it can be identified as the finest topology agreeing with the weak$^*$ topology on bounded sets by Banach-Steinhaus and Banach-Dieudonne. (continued) | |
| Nov 9, 2016 at 13:31 | comment | added | Uri Bader | Indeed, interesting. Could you recommend a good reference for this? | |
| Nov 9, 2016 at 1:03 | history | answered | Cameron Zwarich | CC BY-SA 3.0 |