Question: 6. Let (en) be a complete orthonormal sequence in a Hilbert space H and let (n) be a sequence of scalars. (a) Show that

6. Let (en) be a complete orthonormal sequence in a Hilbert space

6. Let (en) be a complete orthonormal sequence in a Hilbert space H and let (n) be a sequence of scalars. (a) Show that there exists a unique operator T on H such that Te = nen. (b) Show that T is bounded if and only if the sequence (^^) is bounded. (c) For a bounded sequence (n), find the norm of T.

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