Theorems · Theorem · functional analysis
SpectrumRestricts.rightInvOn
∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : Semifield R] [inst_1 : Semifield S] [inst_2 : Ring A]
[inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] {a : A} {f : S → R},
SpectrumRestricts a f → Set.RightInvOn f (⇑(algebraMap R S)) (spectrum S a)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement · cited by 4,706
- spectrumstatement · cited by 510
- Semifieldstatement and proof · cited by 439
- SpectrumRestrictsstatement and proof · cited by 51
- Set.RightInvOnstatement · cited by 47
- QuasispectrumRestricts.rightInvOnproof · cited by 6
- spectrum_subset_quasispectrumproof · cited by 5
- Set.RightInvOn.monoproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- SpectrumRestricts.algebraMap_imageproof · cited by 12
- SpectrumRestricts.starAlgHom_idproof · cited by 2
- NNReal.spectralRadius_mem_spectrumproof · cited by 2
- spectrumRestricts_iffproof · cited by 1