Linear Algebra Done Right · Problem 7C.17

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · positive-operators

Problem

Suppose that T∈L(V)T \in \mathcal{L}(V) is a positive operator. Prove that there exists a polynomial pp with real coefficients such that T=p(T)\sqrt{T} = p(T).

Related theory

Browse the problem library