Question: Suppose that there exists c> 0 such that |(Tr, r)|2 c |r||2 for every r E H. (i) Show thatT is bounded below and

Suppose that there exists c> 0 such that |(Tr, r)|2 c |r||2

Suppose that there exists c> 0 such that |(Tr, r)|2 c |r||2 for every r E H. (i) Show thatT is bounded below and ran T is dense in H. (ii) Show that T is invertible in B(H) and ||T-|| sc.

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