Timeline for Strong topology on a topological vector space
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 8, 2020 at 21:06 | vote | accept | JustWannaKnow | ||
| Jun 8, 2020 at 19:32 | answer | added | Abdelmalek Abdesselam | timeline score: 3 | |
| Jun 8, 2020 at 13:58 | comment | added | Jochen Wengenroth | Yes, that's right. | |
| Jun 8, 2020 at 13:53 | comment | added | JustWannaKnow | @JochenWengenroth this is because, in this topology, a net of operators $T_{\alpha}$ converges to $T$ iff $||T_{\alpha}x-Tx||\to 0$ for every $x \in X$, right? | |
| Jun 8, 2020 at 13:50 | comment | added | Jochen Wengenroth | I consider both names strong operator topology as well as weak$^*$ topology quite unfortunate (although they are of course standard). A good name, IMHO, would be topology of pointwise convergence. | |
| Jun 8, 2020 at 13:47 | history | edited | JustWannaKnow | CC BY-SA 4.0 |
added 9 characters in body
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| Jun 8, 2020 at 13:46 | comment | added | JustWannaKnow | Oh, right. My bad. Gonna fix it right now! Thanks | |
| Jun 8, 2020 at 13:43 | comment | added | Nate Eldredge | Yes, the definitions still make perfect sense for any topological vector space. Reed and Simon probably add the Banach assumption because that's the only case they care about, and because they want to prove theorems that may require that assumption. | |
| Jun 8, 2020 at 13:40 | comment | added | JustWannaKnow | @NateEldredge thanks for the comment! Simon's terminology 'strong operator topology' for $\mathcal{L}(X,\mathbb{C}) = X^{*}$ is defined when $X$ is Banach. Here, you are defining this topology as I proposed? | |
| Jun 8, 2020 at 13:34 | comment | added | Nate Eldredge | If $Y = \mathbb{C}$ then $\mathcal{L}(X,\mathbb{C}) = X^*$ and the strong operator topology on $\mathcal{L}(X, \mathbb{C})$ is the same as the weak-* topology on $X^*$. It's more usual to use the latter name. | |
| Jun 8, 2020 at 13:26 | history | asked | JustWannaKnow | CC BY-SA 4.0 |