Measure, Integration & Real Analysis · Problem 10B.17

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · self-adjoint-operators-norm

Problem

Prove that if

T

is a self-adjoint operator on a Hilbert space, then

\|T^n\| = \|T\|^n

for every

n \in \mathbf{Z}^+