Theorems · Theorem · functional analysis

CFC.exp_log

∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A]
  [inst_3 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_4 : PartialOrder A] [StarOrderedRing A]
  [NonnegSpectrumClass ℝ A] (a : A),
  autoParam (IsStrictlyPositive a) CFC.exp_log._auto_1 → NormedSpace.exp (CFC.log a) = a

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedRing StarRing NormedAlgebra ContinuousFunctionalCalculus PartialOrder StarOrderedRing NonnegSpectrumClass

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Realstatement and proof · cited by 25,697
PartialOrderstatement and proof · cited by 6,410
Set.imageproof · cited by 5,609
StarRingstatement and proof · cited by 1,686
NormedAlgebrastatement and proof · cited by 1,165
Real.logproof · cited by 939
NormedRingstatement and proof · cited by 924
Real.expproof · cited by 871
StarOrderedRingstatement and proof · cited by 587
IsSelfAdjointstatement and proof · cited by 545
spectrumproof · cited by 510
ContinuousFunctionalCalculusstatement and proof · cited by 331

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