 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-2/12e/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

For

1 \leq p < q < \infty

\frac{∥ x ^{(N)} ∥ _{p}}{∥ x ^{(N)} ∥ _{q}} = N^{1/ p - 1/ q} ⟶ \infty.

One of the two inequalities required for equivalent norms therefore fails. Hence

no pair 1 \leq p < q < \infty gives Lipschitz-equivalent norms on V .

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