Linear Algebra Done Right · Problem 7D.4

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · isometries-unitary-operators

Problem

Suppose

\mathbf{F} = \mathbf{C}

and

A, B \in \mathcal{L}(V)

are self-adjoint. Show that

A + iB

is unitary if and only if

AB = BA

and

A^2 + B^2 = I