Theorems · Theorem · functional analysis
SpectrumRestricts.apply_mem
∀ {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} [IsScalarTower R S A],
SpectrumRestricts a f → ∀ {s : S}, s ∈ spectrum S a → f s ∈ spectrum R a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- IsScalarTowerstatement and proof · cited by 3,896
- spectrumstatement and proof · cited by 510
- Semifieldstatement and proof · cited by 439
- SpectrumRestrictsstatement and proof · cited by 51
- SpectrumRestricts.imageproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- cfc_tsubproof · cited by 1
- IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitaryproof · cited by 0