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April 29th, 2013, 08:28 AM   #1
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Kakutani Theorem (functional analysis)

Could someone assist in explaining the reasoning behind the highlighted text of the attached document. Thanks for any assistance.

The attached document has two theorems from the book by Haim Brezis called "Functional Analysis, Sobolev Spaces and Partial Differential Equations"
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April 29th, 2013, 12:46 PM   #2
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Re: Kakutani Theorem (functional analysis)

Let F = E* and apply Theorem 3.16 with F in place of E. So then the "E*" in Theorem 3.16 really means F*, which is of course E**. (The symbol "E" does not represent the same space in each theorem.)
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