Linear Algebra Done Right · Problem 7A.4

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · adjoints

Problem

Suppose

T \in \mathcal{L}(V)

and

U

is a subspace of

V

. Prove that

U \text{ is invariant under } T \iff U^\perp \text{ is invariant under } T^*.