Theorems · Theorem · functional analysis
AlgHom.norm_apply_le_self
∀ {𝕜 : Type u_1} {A : Type u_2} {F : Type u_3} [inst : NormedField 𝕜] [inst_1 : NormedRing A]
[inst_2 : NormedAlgebra 𝕜 A] [CompleteSpace A] [NormOneClass A] [inst_5 : FunLike F A 𝕜] [AlgHomClass F 𝕜 A 𝕜] (f : F)
(a : A), ‖f a‖ ≤ ‖a‖- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- FunLikestatement and proof · cited by 2,560
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NormedRingstatement and proof · cited by 924
- NormOneClassstatement and proof · cited by 136
- AlgHomClassstatement and proof · cited by 50
- spectrum.norm_le_norm_of_memproof · cited by 11
- AlgHom.apply_mem_spectrumproof · cited by 5
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