Theorems · Theorem · functional analysis
SpectrumRestricts.nnreal_iff_nnnorm
∀ {A : Type u_1} [inst : CStarAlgebra A] {a : A} {t : NNReal},
IsSelfAdjoint a → ‖a‖₊ ≤ t → (SpectrumRestricts a ⇑ContinuousMap.realToNNReal ↔ ‖(algebraMap ℝ A) ↑t - a‖₊ ≤ t)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- ENNRealproof · cited by 9,879
- Algebra.algebraMapstatement and proof · cited by 4,706
- NNRealstatement and proof · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- NNNorm.nnnormstatement and proof · cited by 952
- IsSelfAdjointstatement and proof · cited by 545
- CStarAlgebrastatement and proof · cited by 123
Cited by2
Results whose statement or proof uses this declaration.
- SpectrumRestricts.nnreal_addproof · cited by 2
- CStarAlgebra.isClosed_nonnegproof · cited by 0