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Apr 14, 2021 at 8:35 comment added Dirk True - and luckily, that's exactly what was asked for… Thanks for the catch!
Apr 14, 2021 at 8:35 history edited Dirk CC BY-SA 4.0
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Apr 13, 2021 at 17:37 comment added gerw I don't think that this is true (unless $X$ is reflexive). The conjugate of the preconjugate is always weak-* lower semicontinuous. Hence, you have to assume at least that $g$ is weak-* lower semicontinuous.
Apr 4, 2021 at 18:50 vote accept e.lipnowski
Apr 4, 2021 at 14:42 history answered Dirk CC BY-SA 4.0