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Let ℋ be a Hilbert space and let {en : n ≥ 1} be an orthonormal basis of ℋ. Suppose T:ℋ → ℋ is a bounded linear operator. Which of the following CANNOT be true?
Options:
A .  T(en) = e1 for all n ≥ 1
B .  T(en) = en+1 for all n ≥ 1
C .  T(en) = √(n+1)/n en for all n ≥ 1
D .  T(en) = en-1 for all n ≥ 2 and T(e1) = 0
Answer: Option A


-NA-


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