Theorems · Theorem · functional analysis
AlgHom.toContinuousLinearMap_norm
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[inst_3 : CompleteSpace A] [NormOneClass A] (φ : A →ₐ[𝕜] 𝕜), ‖φ.toContinuousLinearMap‖ = 1- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- AlgHomstatement and proof · cited by 3,236
- one_mulproof · cited by 2,841
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- map_oneproof · cited by 861
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