Linear Algebra Done Right · Problem 7A.2

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · adjoints

Problem

Suppose T∈L(V,W)T \in \mathcal{L}(V, W). Prove that T=0  ⟺  T∗=0  ⟺  T∗T=0  ⟺  TT∗=0.T = 0 \iff T^* = 0 \iff T^*T = 0 \iff TT^* = 0.

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