Measure, Integration & Real Analysis · Problem 10B.13

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · normal-operators-norm

Problem

Prove or give a counterexample: If

T

is a normal operator on a Hilbert space and

T = A + iB

, where

A

and

B

are self-adjoint, then

\|T\| = \sqrt{\|A\|^2 + \|B\|^2}