Hi The question is: Find an example of and a sequence which converges strongly to 0 in , and weakly but not strongly in . Any help would be greatly appreciated.
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Originally Posted by markwolfson16900 Hi The question is: Find an example of and a sequence which converges strongly to 0 in , and weakly but not strongly in . If p < q and in then in . So for your example you need to take q < p. Suppose for example that q = 2 and p = 4. Define the k'th coordinate of by Then , so strongly in . But , so strongly in . I'll leave it to you to figure out why weakly in .
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