Linear Algebra Done Right · Problem 7C.11

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · positive-operators

Problem

Suppose

T

is a positive operator on

V

and

U

is a subspace of

V

invariant under

T

. Prove that

T|_U \in \mathcal{L}(U)

is a positive operator on

U