Linear Algebra Done Right · Problem 7B.6

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose

V

is a complex inner product space and

T \in \mathcal{L}(V)

is a normal operator such that

T^9 = T^8

. Prove that

T

is self-adjoint and

T^2 = T