Measure, Integration & Real Analysis · Problem 10B.15
Linear Maps on Hilbert Spaces — Sheldon Axler
Mathematics — Measure Theory · normal-operators-spectrum
Problem
Suppose T is a normal operator on a Hilbert space.
((a)) Prove that if α is an eigenvalue of T, then ∣α∣2 is an eigenvalue of T∗T.
((b)) Prove that if α∈sp(T), then ∣α∣2∈sp(T∗T).