Theorems · Theorem · functional analysis
IsSelfAdjoint.sq_spectrumRestricts
∀ {A : Type u_1} [inst : CStarAlgebra A] {a : A},
IsSelfAdjoint a → SpectrumRestricts (a ^ 2) ⇑ContinuousMap.realToNNReal- Cited by
- 1 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.imageproof · cited by 5,609
- NNRealstatement · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- IsSelfAdjointstatement and proof · cited by 545
- spectrumproof · cited by 510
- continuous_id'proof · cited by 295
- CStarAlgebrastatement and proof · cited by 123
- continuousOn_id'proof · cited by 109
- sq_nonnegproof · cited by 106
Cited by1
Results whose statement or proof uses this declaration.
- spectrum_star_mul_self_nonnegproof · cited by 1