Timeline for Dual of essentially compactly supported functions on a hemi-compact Radon space
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| S Jun 17, 2021 at 15:06 | history | bounty ended | CommunityBot | ||
| S Jun 17, 2021 at 15:06 | history | notice removed | CommunityBot | ||
| Jun 9, 2021 at 16:52 | comment | added | Jochen Wengenroth | If $X$ is compact, the dual of $L^1(X,\mu)$ is $L^\infty(X,\mu)$. In the hemi-compact case, the dual is the projective limit of $L^\infty(X_n,\mu)$. What else do you want? Somewhat artificially, you can identify $L^\infty(X,\mu)$ with a space of measures, assigning to each bounded function $f$ the measure with $\mu$-density $f$. | |
| S Jun 9, 2021 at 13:31 | history | bounty started | Catologist_who_flies_on_Monday | ||
| S Jun 9, 2021 at 13:31 | history | notice added | Catologist_who_flies_on_Monday | Authoritative reference needed | |
| Jun 8, 2021 at 12:06 | comment | added | Catologist_who_flies_on_Monday | @JochenWengenroth I was especially wondering if it had an interpretation as some sort of (Radon?) measures... do you think so? Also yes to your first point. | |
| Jun 8, 2021 at 12:05 | history | edited | Catologist_who_flies_on_Monday | CC BY-SA 4.0 |
added 7 characters in body
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| Jun 4, 2021 at 16:14 | comment | added | Jochen Wengenroth | Roughly, the dual of the LB-space is the projective limit of the duals. My guess is thus, that $L_c(X)'$ is the space of measurable function whose restrictions to all $X_n$ are $\mu$-a.e. bounded. | |
| Jun 4, 2021 at 16:11 | comment | added | Jochen Wengenroth | Do you really mean the category of locally convex spaces and continuous maps or rather the continuous and linear maps? Moreover, $X_n$ is probably a compact exhaustion of $X$, right? | |
| Jun 4, 2021 at 11:43 | history | asked | Catologist_who_flies_on_Monday | CC BY-SA 4.0 |