FA14

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Let X=l^{2}\, and e_{n}=(0,..,0,1,0,...)\, where 1 is in the n\,th position. Define T_{n}x=\xi _{n}\, for x=(\xi _{j})\in l^{2}\,. Show that T_{n}x\to 0\, for each x\,, but ||T_{n}-0||\not \to 0\,.