 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-323/4/c/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The two forms of

ω_{A B}

found in part (i) give

(1 + ε) ω_{A B} - ρ_{A B} = X_{-} \geq 0, (1 + ε) ω_{A B} - σ_{A B} = X_{+} \geq 0.

Therefore, in the Löwner order,

ρ_{A B} \leq (1 + ε) ω_{A B}, σ_{A B} \leq (1 + ε) ω_{A B} .

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