Linear Algebra Done Right · Problem 7F.19

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms

Problem

Prove that if T∈L(V,W)T \in \mathcal{L}(V, W), then ∥T∗T∥=∥T∥2\|T^*T\| = \|T\|^2. This formula for ∥T∗T∥\|T^*T\| leads to the important subject of C∗C^*-algebras.

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