Theorems · Theorem · functional analysis
AlgHom.apply_mem_spectrum
∀ {F : Type u_1} {R : Type u_2} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A]
[inst_3 : FunLike F A R] [AlgHomClass F R A R] [Nontrivial R] (φ : F) (a : A), φ a ∈ spectrum R a- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 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 and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- FunLikestatement and proof · cited by 2,560
- Nontrivialstatement and proof · cited by 2,416
- sub_selfproof · cited by 996
- RingHomClass.toRingHomproof · cited by 746
- map_subproof · cited by 565
- spectrumstatement · cited by 510
Cited by5
Results whose statement or proof uses this declaration.
- WeakDual.CharacterSpace.mem_spectrum_iff_existsproof · cited by 2
- WeakDual.CharacterSpace.apply_mem_spectrumproof · cited by 1
- AlgHom.norm_apply_le_selfproof · cited by 0
- AlgHom.norm_apply_le_self_mul_norm_oneproof · cited by 0
- AlgHom.toContinuousLinearMap_normproof · cited by 0