Theorems · Theorem · functional analysis
IsSelfAdjoint.quasispectrumRestricts
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : NonUnitalRing A] [inst_2 : StarRing A] [inst_3 : Module ℂ A]
[inst_4 : IsScalarTower ℂ A A] [inst_5 : SMulCommClass ℂ A A] [NonUnitalContinuousFunctionalCalculus ℂ A IsStarNormal]
{a : A}, IsSelfAdjoint a → QuasispectrumRestricts a ⇑Complex.reCLM- Cited by
- 6 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalRingstatement and proof · cited by 422
Cited by6
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.spectrumRestrictsproof · cited by 13
- cfcₙ_real_eq_complexproof · cited by 3
- quasispectrum_imaginaryPart'proof · cited by 1
- quasispectrum_realPart'proof · cited by 1
- cfcₙHom_real_eq_restrictstatement and proof · cited by 0
- cfcₙ_complex_eq_realproof · cited by 0