Linear Algebra Done Right · Problem 7F.13

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms-positive

Problem

Suppose

S, T \in \mathcal{L}(V)

are positive operators. Show that

\|S - T\| \leq \max\{\|S\|, \|T\|\} \leq \|S + T\|.