 Solution

ID: past-exam-of-the-analysis-course-of-the-university-of-oxford/2011/6/b/i/solution

Expanding both squared norms gives

∥ (I + T) x ∥^{2} - ∥ (I - T) x ∥^{2} = 4 Re ⟨ T x, x ⟩ \geq 0.

Both norms are nonnegative, so taking square roots proves

∥ (I + T) x ∥ \geq ∥ (I - T) x ∥

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