How do I show that a Banach space $X$ is reflexive if its dual $X'$ is reflexive without using any deep functional analysis theorems?
Reflexive Banach Spaces
2
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functional-analysis
banach-spaces
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0Could you be more precise when you say "deep functional analysis theorems"? Perhaps you could state (the names of) result that you are not willing to use. – 2012-11-07
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0Also, you may find http://math.stackexchange.com/questions/152343/a-question-about-banach-reflexive-space helpful. – 2012-11-07
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0I don't want to use Banach-Alaoglu-Bourbaki theorem, anything related to the Baire Category Theorem, or the Hanh-Banach Theorem. – 2012-11-07
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0@Parkee then you should stop doing mathematics. I'm really hate question like "Prove everything without using anything." Well, one can do that, but this "proof" will repeat standard arguments of Hahn-Banach or Banach-Alaoglu or whatever else, and what is more it will be very long. – 2012-11-07
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0The problem was found in a book that hadn't introduced any of these theorems yet. I don't want to prove it with machinery that the book hasn't introduced in case there is an important concept that I need to employ to prove it that I don't currently grasp. – 2012-11-07
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2@Parakee So what has developed your book? – 2012-11-07