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Theorem 3 If (m) is an orthonormal sequence in a Hilbert space H and (u: at) = U each n E N implies u =

Theorem 3 If (m) is an orthonormal sequence in a Hilbert space H and (u: at\") = U each n E N implies u = (L then (n) is complete (or total) in H. Remark The sequence (bk given by (354:5) : V2?" sin(E_1k7rz), is not complete in 2(E,F). Explain

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