Theorems · Theorem · functional analysis
IsGreatest.nnnorm_cfc_nnreal
∀ {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] [Nontrivial A] (f : NNReal → NNReal) (a : A),
autoParam (ContinuousOn f (spectrum NNReal a)) IsGreatest.nnnorm_cfc_nnreal._auto_1 →
autoParam (0 ≤ a) IsGreatest.nnnorm_cfc_nnreal._auto_3 → IsGreatest (f '' spectrum NNReal a) ‖cfc f a‖₊- Cited by
- 5 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Set.imagestatement and proof · cited by 5,609
- NNRealstatement and proof · cited by 4,310
- Nontrivialstatement and proof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- ContinuousOnstatement and proof · cited by 1,411
- NNReal.toRealproof · cited by 1,260
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement and proof · cited by 952
Cited by5
Results whose statement or proof uses this declaration.
- apply_le_nnnorm_cfc_nnrealproof · cited by 3
- nnnorm_cfc_nnreal_ltproof · cited by 1
- nnnorm_cfc_nnreal_leproof · cited by 1
- IsometricContinuousFunctionalCalculus.isGreatest_spectrumproof · cited by 1
- MonotoneOn.nnnorm_cfcproof · cited by 0