Theorems · Theorem · functional analysis
cfc_im_id
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[inst_4 : StarModule ℂ A] [inst_5 : ContinuousFunctionalCalculus ℂ A IsStarNormal] (a : A),
autoParam (IsStarNormal a) cfc_im_id._auto_1 → cfc (fun x => ↑x.im) a = ↑(imaginaryPart a)- Cited by
- 3 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.
Cites39
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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- mul_commproof · cited by 2,262
- StarRingstatement and proof · cited by 1,686
Cited by3
Results whose statement or proof uses this declaration.
- spectrum_imaginaryPartproof · cited by 2
- cfc_imaginaryPartproof · cited by 0
- cfc_comp_improof · cited by 0