Theorems · Theorem · functional analysis

CFC.isStrictlyPositive_conjSqrt_iff

∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : TopologicalSpace A]
  [inst_4 : StarOrderedRing A] [inst_5 : Algebra ℝ A] [inst_6 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
  [inst_7 : NonnegSpectrumClass ℝ A] [inst_8 : SeparatelyContinuousMul A] [IsSemitopologicalRing A] [T2Space A]
  (c a : A),
  autoParam (IsStrictlyPositive c) CFC.isStrictlyPositive_conjSqrt_iff._auto_1 →
    (IsStrictlyPositive ((CFC.conjSqrt c) a) ↔ IsStrictlyPositive a)

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.ConjSqrt
Cited by: 0 results in Mathlib
Foundations: Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PartialOrder Ring StarRing TopologicalSpace StarOrderedRing Algebra ContinuousFunctionalCalculus NonnegSpectrumClass SeparatelyContinuousMul IsSemitopologicalRing T2Space

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DFunLike.coestatement · cited by 62,936
Realstatement and proof · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
RingHom.idstatement · cited by 18,349
Algebrastatement and proof · cited by 11,388
Ringstatement and proof · cited by 7,463
PartialOrderstatement and proof · cited by 6,410
ContinuousLinearMapstatement · cited by 5,352
StarRingstatement and proof · cited by 1,686
T2Spacestatement and proof · cited by 1,351
StarOrderedRingstatement and proof · cited by 587
IsSelfAdjointstatement and proof · cited by 545

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