space Suppose that (Tx, x) > 0 for all x H. 1. Let (zn)n1 be a sequence of H that converges to 0. Suppose that (Tn)n>1 converge to LEH. (a) Show that (L, h) + (Th, h) >0 for all h € H. (b) Deduce that L=0. (Hint: replace h by sh for all e > 0).

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