Timeline for Jacobson density theorem and Riesz representation theorem
Current License: CC BY-SA 4.0
11 events
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| Jun 9, 2021 at 1:24 | comment | added | paul garrett | In light of actual mathematical facts, this question turns out to be too broad, yes, but in a different universe it the answer would have been that the two things are indeed the same. So, why not here? I myself find this a fair question. :) | |
| Jun 9, 2021 at 0:58 | comment | added | Yemon Choi | I think there is no meaningful connection other than saying that some injection from a class of maps into another class is surjective. This seems hopelessly broad. | |
| Jun 9, 2021 at 0:35 | comment | added | IJM98 | @MarkWildon Well as the first comment from Sasha, Riesz implies also that $V\longrightarrow V^*$ is surjective, so maybe there is something. | |
| S Jun 8, 2021 at 22:39 | history | suggested | Dirk Werner | CC BY-SA 4.0 |
some language
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| Jun 8, 2021 at 20:42 | review | Suggested edits | |||
| S Jun 8, 2021 at 22:39 | |||||
| Jun 8, 2021 at 12:39 | comment | added | IJM98 | @MarkWildon It doesn't seem like there is a parallel. | |
| Jun 8, 2021 at 12:22 | comment | added | Mark Wildon | Is there a parallel in their corollaries? JDT (in the version you've stated above) implies that the canonical map $R \rightarrow \mathrm{End}_D(U)$ is surjective (which is how the result is often stated); Riesz implies the existence of an adjoint to an arbitrary bounded linear transformation on $H$. | |
| Jun 8, 2021 at 6:05 | comment | added | Sasha | I personally don't see too much similarity. Jacobson is of the type "given a nice $A$-module $M$, the canonical $A \to End_{End_A (M)} (M)$ is surjective". Riesz is of the type "Given $V \to V^*$ with some nice properties (in particular, being injective), $V \to V^*$ is surjective". But maybe I miss something. | |
| Jun 8, 2021 at 0:17 | history | edited | IJM98 |
edited tags
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| Jun 7, 2021 at 23:31 | history | edited | IJM98 |
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| Jun 7, 2021 at 18:47 | history | asked | IJM98 | CC BY-SA 4.0 |