Linear Algebra Done Right · Problem 7B.12

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose

V

is a complex vector space and

T \in \mathcal{L}(V)

is normal. Prove that if

S

is an operator on

V

that commutes with

T

, then

S

commutes with

T^*

. The result in this exercise is called Fuglede's theorem.