Theorems · Theorem · functional analysis
nnnorm_cfc_nnreal_lt
∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A] [inst_3 : PartialOrder A]
[inst_4 : StarOrderedRing A] [inst_5 : IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
[inst_6 : NonnegSpectrumClass ℝ A] {f : NNReal → NNReal} {a : A} {c : NNReal},
0 < c → (∀ x ∈ spectrum NNReal a, f x < c) → ‖cfc f a‖₊ < c- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Set.imageproof · cited by 5,609
- NNRealstatement and proof · cited by 4,310
- Nontrivialproof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- ContinuousOnproof · cited by 1,411
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement and proof · cited by 952
- NormedRingstatement and proof · cited by 924
- StarOrderedRingstatement and proof · cited by 587
Cited by1
Results whose statement or proof uses this declaration.
- nnnorm_cfc_nnreal_lt_iffproof · cited by 0