For $\displaystyle p>1$, is there a sequence $\displaystyle {x_n} \in l^p$ and $\displaystyle x \in l^p$ such that $\displaystyle x_n \rightarrow x$ weakly but $\displaystyle x_n \not \rightarrow x$ strongly?

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- Apr 24th 2009, 08:02 PMdori1123weak convergence
For $\displaystyle p>1$, is there a sequence $\displaystyle {x_n} \in l^p$ and $\displaystyle x \in l^p$ such that $\displaystyle x_n \rightarrow x$ weakly but $\displaystyle x_n \not \rightarrow x$ strongly?