Timeline for A characterization of $L_1(\mu)$ in $L_\infty(\mu)^*$
Current License: CC BY-SA 4.0
18 events
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| Jan 9, 2020 at 16:26 | comment | added | Sergei Akbarov | Robert thank you! @billabong you drew my attention to Stack spaces, so that was useful. Excuse me. | |
| May 28, 2018 at 19:01 | comment | added | Robert Furber | @billabong Oh, I see. I got confused by your first sentence because some people call the $\sigma(L^\infty,L^1)$-topology the $L^1$-topology. You are referring to what J. B. Cooper calls the $\beta_1$ topology and Proposition 1.6 of chapter III? Then by Corollary 1.9 we are talking about $\tau(L^\infty,L^1)$, the Mackey topology. Also, Cooper defines this for locally compact spaces only, not measure spaces. | |
| May 28, 2018 at 18:23 | comment | added | billabong | Sadly, I can't delete it. Maybe some nice moderator could take pity on me. | |
| May 28, 2018 at 18:18 | comment | added | billabong | The strict topology I mentioned is NOT the bounded weak $\ast$ topology. How I regret posting this answer!!! | |
| May 28, 2018 at 11:09 | comment | added | Robert Furber | @SergeiAkbarov The mixed topology is exactly the bounded weak-* topology, i.e. this answer considers $L^\infty$ as a Smith space. | |
| May 28, 2018 at 7:54 | review | Low quality posts | |||
| May 28, 2018 at 10:44 | |||||
| May 28, 2018 at 7:50 | history | edited | billabong | CC BY-SA 4.0 |
have reformulated my reply
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| May 28, 2018 at 7:32 | comment | added | billabong | See chapter III of the monograph "Saks spaces and applications to functional analysis". | |
| May 28, 2018 at 6:53 | comment | added | Sergei Akbarov | If what I guess is what you had in mind (or if there is another similar criterion), then you should roll back your answer and formulate the result explicitly. You can also contact me directly by email, if you have doubts. | |
| May 28, 2018 at 6:36 | comment | added | Sergei Akbarov | Billabong, excuse me I could not reply earlier. That is interesting, but I did not understand, what the result is exactly. If $\tau$ is a topology on $L_\infty(\mu)$ such that $(L_\infty(\mu),||\cdot||_\infty,\tau)$ is a Saks space, then $L_1(\mu)$ is the space of functionals on $L_\infty(\mu)$ continuous with respect to $\tau$? Is that what you mean? And where is this written? | |
| May 28, 2018 at 5:38 | review | First posts | |||
| May 28, 2018 at 6:40 | |||||
| May 27, 2018 at 22:07 | review | Low quality posts | |||
| May 28, 2018 at 3:55 | |||||
| May 27, 2018 at 22:06 | history | edited | billabong | CC BY-SA 4.0 |
deleting for reasons stated above
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| May 27, 2018 at 20:35 | comment | added | billabong | The article by Saks is simply called "On some functionals". It is so celebrated that you will get an immmediate hit as a pdf file by simply googling the author's name and the title. It appeared in one of the AMS journals in the 30's of the last century. | |
| May 27, 2018 at 20:29 | comment | added | billabong | simply google under Saks spaces. It even has an MOS classification number. The paper of Saks is also easy to trace. | |
| May 27, 2018 at 20:26 | history | edited | billabong | CC BY-SA 4.0 |
added more details
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| May 27, 2018 at 20:25 | comment | added | Sergei Akbarov | billabong, could you, please, give some references? | |
| May 27, 2018 at 20:20 | history | answered | billabong | CC BY-SA 4.0 |