Measure, Integration & Real Analysis · Problem 10B.11

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · normal-self-adjoint-projections

Problem

Suppose

P

is a bounded operator on a Hilbert space

V

such that

P^2 = P

. Prove that

P

is self-adjoint if and only if

P

is normal.