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January 21st, 2014, 05:30 AM   #1
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Weak Convergence Question

I just want to confirm that if we have a normed spaces and and (X subset Y) then does it follow that if weakly in then weakly in ? Thanks.
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January 21st, 2014, 03:16 PM   #2
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Re: Weak Convergence Question

. But . Given , then which means . Thus, your claim is correct, given that and are both Banach.
(Peterpan - have you found some neat application of the weak topology and weak convergence?)
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