Timeline for Convergence of convex combinations in topological vector spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2015 at 12:04 | comment | added | Marcel Schmidt | @Jochen Wengenroth I am quite aware that subnets are much more flexible. Unfortunately, I was not able to employ this. | |
| Sep 25, 2015 at 10:20 | comment | added | Jochen Wengenroth | You probably know that the notion of a subnet is quite different from that of a subsequence. In particular, the index set of the subnet can be very different. I don't know however, if this is helpful. | |
| Sep 25, 2015 at 9:36 | comment | added | Marcel Schmidt | @Jochen Wengenroth Thanks for the advice, I have already tried that. In fact, in the $L^0(m)$ case there is a very explicit description of a system of topology generating F-norms. For a set of finite $m$-measure $U$ one lets $$\|f\|_U = \int_U |f|\wedge 1\, {\rm d} m $$ These $\|\cdot\|_U$ then induce the topology. However, I do not really see how to apply the idea of Lemma 2 to an arbitrary convergent net and all these $F$-norms at once. | |
| Sep 24, 2015 at 20:56 | comment | added | Jochen Wengenroth | Isn't there a family of so-called F-norms (look at Köthe's or Jarchow's book) which induces the topology? Perhaps you can then use the idea of Lemma 2. | |
| Sep 24, 2015 at 16:21 | review | First posts | |||
| Sep 24, 2015 at 16:25 | |||||
| Sep 24, 2015 at 16:17 | history | asked | Marcel Schmidt | CC BY-SA 3.0 |