Theorems · Theorem · functional analysis

CFC.continuousOn_log

∀ {A : Type u_2} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A]
  [inst_3 : IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [ContinuousStar A] [CompleteSpace A],
  ContinuousOn CFC.log {a | IsSelfAdjoint a ∧ IsUnit a}

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedRing StarRing NormedAlgebra IsometricContinuousFunctionalCalculus ContinuousStar CompleteSpace

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Realstatement and proof · cited by 25,697
Set.ofPredstatement and proof · cited by 6,101
Compl.complproof · cited by 2,925
CompleteSpacestatement and proof · cited by 2,532
Set.iUnionproof · cited by 2,483
StarRingstatement and proof · cited by 1,686
IsUnitstatement and proof · cited by 1,602
ContinuousOnstatement · cited by 1,411
NormedAlgebrastatement and proof · cited by 1,165
Real.logproof · cited by 939
NormedRingstatement and proof · cited by 924
IsSelfAdjointstatement and proof · cited by 545

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