Timeline for When is the norm of all positive operators on an ordered Banach space determined by their values on the positive cone?
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| Oct 20, 2015 at 14:16 | answer | added | Anthony Wickstead | timeline score: 7 | |
| Nov 3, 2012 at 11:15 | vote | accept | Miek Messerschmidt | ||
| Nov 3, 2012 at 11:14 | answer | added | Miek Messerschmidt | timeline score: 3 | |
| Mar 21, 2012 at 17:15 | history | edited | Miek Messerschmidt | CC BY-SA 3.0 |
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| Mar 6, 2012 at 9:20 | comment | added | Miek Messerschmidt | Although I'm hardly an expert on the machinery, I think the reference* below answers your question, Matthew. As long as we assume the cone to be normal, we get "enough" positive functionals so that the dual cone/wedge is generating in the dual. From there we are able to make lots of positive of rank 1 operators. (Quickly browsing through the proof I see it does depend on some a separation theorem, so yes, does look like it depends on Hahn Banach.) *Cones & Duality by Aliprantis & Tourky books.google.nl/books?id=EGNzDiCJ3zAC&lpg=PP1&pg=PA78 | |
| Mar 6, 2012 at 7:43 | comment | added | Matthew Daws | Can you explain why there are any non-zero positive operators? I presume we find a positive functional; and I presume we use Hahn-Banach for this, but I just don't see how right now... | |
| Mar 5, 2012 at 15:07 | history | edited | Miek Messerschmidt | CC BY-SA 3.0 |
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| Mar 5, 2012 at 13:38 | history | edited | Miek Messerschmidt | CC BY-SA 3.0 |
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| Mar 5, 2012 at 13:33 | history | asked | Miek Messerschmidt | CC BY-SA 3.0 |