I saw some proves here relying on "uniform boundedness", but "uniform boundedness" is aplly to complete spaces("Baire thorem").
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What are you asking? – copper.hat Feb 04 '17 at 21:31
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Weak convergence implies boundedness in norm vector space?I wanted to mentiond that I saw some proves here but I don't think them correct because of completeness. – Yarden Sharabi Feb 04 '17 at 21:37
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This might help? http://math.stackexchange.com/a/695469/27978 – copper.hat Feb 04 '17 at 21:57
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No because that's again a proof that using "uniform boundedness" which is realy working in that case because the space Lp is complete. – Yarden Sharabi Feb 04 '17 at 22:03
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Read the last line of the answer. The point is that the dual is always complete. – copper.hat Feb 04 '17 at 22:04
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thank you very much for your help! – Yarden Sharabi Feb 04 '17 at 22:08
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You are very welcome, good luck! – copper.hat Feb 04 '17 at 22:10