Theorems · Theorem · functional analysis
WeakDual.CharacterSpace.mem_spectrum_iff_exists
∀ {A : Type u_1} [inst : NormedCommRing A] [inst_1 : NormedAlgebra ℂ A] [CompleteSpace A] {a : A} {z : ℂ},
z ∈ spectrum ℂ a ↔ ∃ f, f a = z- Cited by
- 2 results in Mathlib
- Foundations
- Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.Elemstatement and proof · cited by 7,166
- Complexstatement and proof · cited by 5,565
- Algebra.algebraMapproof · cited by 4,706
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- map_subproof · cited by 565
- spectrumstatement and proof · cited by 510
- NormedCommRingstatement and proof · cited by 218
- WeakDualstatement · cited by 103
- WeakDual.characterSpacestatement and proof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- spectrum.gelfandTransform_eqproof · cited by 1
- StarAlgebra.elemental.bijective_characterSpaceToSpectrumproof · cited by 0