Theorems · Theorem · functional analysis

CFC.ringInverse_conjSqrt

∀ {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.ringInverse_conjSqrt._auto_1 →
    Ring.inverse ((CFC.conjSqrt c) a) = (CFC.conjSqrt (Ring.inverse c)) (Ring.inverse a)

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.ConjSqrt
Cited by: 1 results in Mathlib
Foundations: Depth 223 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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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · 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
map_zeroproof · cited by 1,614
IsUnitproof · cited by 1,602
T2Spacestatement and proof · cited by 1,351

Cited by1

Results whose statement or proof uses this declaration.

CStarAlgebra.convexOn_ringInverseproof · cited by 1