Timeline for What is the "Krein-Milman theorem for cones"?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2022 at 12:32 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| May 6, 2010 at 20:55 | comment | added | Matthew Daws | Jonas: Yep, I agree, we could just look at the complex numbers! Also not sure why that didn't occur to me... | |
| May 6, 2010 at 19:53 | comment | added | Jonas Meyer | In retrospect, couldn't we simplify the example by taking $V=\mathbb{C}$? I like your example, but this makes it all the more sad that I didn't realize the problem. | |
| May 6, 2010 at 19:16 | comment | added | Jonas Meyer | I finally got a chance to come back to this. To finish the argument (which as I mentioned in the last comment only requires $s(x)\ngeq0$), I can just break it up into cases depending on whether or not $(x+x^*)/2, (x-x^*)/(2i)$ are in $C$. Perhaps this is what Paulsen had in mind, but he just forgot to mention the reduction (or implicitly left it to the reader). "Krein-Milman" might have just been a slip where "Hahn-Banach" was intended, and it's not too surprising that it would be repeated in 2 very similar arguments (the other being on page 77). Thanks again for the answer. | |
| May 6, 2010 at 19:07 | vote | accept | Jonas Meyer | ||
| May 6, 2010 at 13:12 | comment | added | Jonas Meyer | Thanks! I still don't know what was meant by Krein-Milman; I had suspected it was a typo, but I just noticed that the same invocation occurs in a previous chapter. The case $x*=x$ isn't quite enough, but all that is really needed is $s(x)\ngeq0$. Thanks again for pointing out that the statement isn't correct. I have to leave the computer now for a while. | |
| May 6, 2010 at 12:34 | history | edited | Matthew Daws | CC BY-SA 2.5 |
Fixed LaTeX
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| May 6, 2010 at 12:23 | history | answered | Matthew Daws | CC BY-SA 2.5 |