Theorems · Theorem · functional analysis
NormedSpace.algebraMap_exp_comm
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕂] [inst_1 : CharZero 𝕂] [ContinuousSMul ℚ 𝕂]
[inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝕂] (x : 𝕂),
(algebraMap 𝕂 𝔸) (NormedSpace.exp x) = NormedSpace.exp ((algebraMap 𝕂 𝔸) x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Algebra.algebraMapstatement · cited by 4,706
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- ContinuousSMulstatement and proof · cited by 1,016
- CharZerostatement and proof · cited by 932
- NormedRingstatement and proof · cited by 924
- NormedSpace.expstatement · cited by 157
- edist_lt_topproof · cited by 32
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- spectrum.exp_mem_expproof · cited by 1