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3. Define T:l2 by, == where No = Nu(0). Prove that where |-|2 denotes the norm in I2 and the norm in C 6. Let H be a separable Hilbert space and (ex)REM be anorthonormal basis for H. (i) By considering - for any k,1 E N with k + 1, deduce if the sequence (ex)REN can have a limit in H or not. (ii) Explain why for all I E H we have, lim (r,ex) = 0.

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