Theorems · Theorem · functional analysis
CFC.exp_eq_normedSpace_exp
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : RCLike 𝕜] {p : A → Prop} [inst_1 : NormedRing A] [inst_2 : StarRing A]
[inst_3 : NormedAlgebra 𝕜 A] [inst_4 : ContinuousFunctionalCalculus 𝕜 A p] {a : A},
autoParam (p a) CFC.exp_eq_normedSpace_exp._auto_1 → cfc NormedSpace.exp a = NormedSpace.exp a- Cited by
- 5 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebraproof · cited by 11,388
- Set.Elemproof · cited by 7,166
- RCLikestatement and proof · cited by 2,829
- Continuousproof · cited by 2,592
- ContinuousMapproof · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- ContinuousOnproof · cited by 1,411
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- DFunLikeproof · cited by 576
- spectrumproof · cited by 510
Cited by5
Results whose statement or proof uses this declaration.
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- CFC.real_exp_eq_normedSpace_expproof · cited by 3
- expUnitary_argSelfAdjointproof · cited by 2
- argSelfAdjoint_expUnitaryproof · cited by 0
- CFC.complex_exp_eq_normedSpace_expproof · cited by 0