 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-3/21i/a/solution

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

T : H \to H

, the spectrum is

σ (T) = {λ \in C : T - λ I has no bounded inverse},

while the point spectrum is the set of eigenvalues, equivalently the

λ

for which

T - λ I

is not injective.

T = T^{*}

, or

⟨ T x, y ⟩ = ⟨ x, T y ⟩

for all

x, y \in H

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