Linear Algebra Done Right · Problem 7B.11

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Prove that every self-adjoint operator on

V

has a cube root. An operator

S \in \mathcal{L}(V)

is called a cube root of

T \in \mathcal{L}(V)

S^3 = T