Theorems · Theorem · functional analysis
IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le
∀ {𝕜 : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} [inst : RCLike 𝕜] [inst_1 : NormedRing A]
[inst_2 : StarRing A] [inst_3 : NormedAlgebra 𝕜 A] [IsometricContinuousFunctionalCalculus 𝕜 A p] (a : A) ⦃x : 𝕜⦄,
x ∈ spectrum 𝕜 a → autoParam (p a) IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le._auto_1 → ‖x‖₊ ≤ ‖a‖₊- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NNRealstatement · cited by 4,310
- RCLikestatement and proof · cited by 2,829
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement and proof · cited by 952
- NormedRingstatement and proof · cited by 924
- spectrumstatement and proof · cited by 510
- continuousOn_id'proof · cited by 109
- IsometricContinuousFunctionalCalculusstatement and proof · cited by 62
- cfc_idproof · cited by 20
- nnnorm_apply_le_nnnorm_cfcproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.