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Mar 16, 2020 at 20:25 comment added Sergey Slavnov Hahn-Banach theorem extension theorem cen be adapted to cones with monotone norm. I.e. a bounded positive functional defined on a subcone of a normed cone extends to a positive funnctional on the whole cone of the same norm. (That the norm is monotone is important!!) A proof is very similar to the standard Hahn-Banach for vector spaces. I'll, hopefully post it, when I have more time.
Mar 16, 2020 at 19:05 comment added user44191 It would generally be better to post the proof; you are allowed (and encouraged) to answer your own questions when you think you have the answer.
Mar 16, 2020 at 19:00 review Low quality posts
Mar 16, 2020 at 20:32
Mar 16, 2020 at 18:43 history answered Sergey Slavnov CC BY-SA 4.0