Linear Algebra Done Right · Problem 7F.9

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms-invertibility

Problem

Suppose T∈L(V)T \in \mathcal{L}(V). Prove that for every ϵ>0\epsilon > 0, there exists an invertible operator S∈L(V)S \in \mathcal{L}(V) such that 0<∥T−S∥<ϵ0 < \|T - S\| < \epsilon.

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