(c) For an orthonormal sequence {u} in a Hilbert space H, prove the equivalence of the conditions (i) xlu for all n implies x = 0, (ii) x = Σu for all x € H.

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(c)
For an orthonormal sequence {u} in a
Hilbert space H, prove the equivalence of
the conditions
(i) xlu for all n implies x = 0,
(ii) _x = Σ<x, u₁> u for all x € H.
Transcribed Image Text:(c) For an orthonormal sequence {u} in a Hilbert space H, prove the equivalence of the conditions (i) xlu for all n implies x = 0, (ii) _x = Σ<x, u₁> u for all x € H.
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