Theorems · Theorem · functional analysis
NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero
∀ {F : Type u_1} [inst : NormedRing F] [NormOneClass F] [NormMulClass F] [inst_3 : NormedAlgebra ℂ F] (x : F),
∃ z, ‖x - (algebraMap ℂ F) z‖ = 0If F is a normed ℂ-algebra and x : F, then there is a complex number z such that
‖x - algebraMap ℂ F z‖ = 0 (whence x = algebraMap ℂ F z).
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- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
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