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January 21st, 2014, 05:30 AM  #1 
Newbie Joined: Mar 2013 Posts: 16 Thanks: 0  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.

January 21st, 2014, 03:16 PM  #2 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  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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