Theorems · Theorem · functional analysis
CFC.conjSqrt_apply
∀ {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] {c a : A},
(CFC.conjSqrt c) a = CFC.sqrt c * a * CFC.sqrt c- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- ContinuousFunctionalCalculusstatement and proof · cited by 331
Cited by2
Results whose statement or proof uses this declaration.
- CFC.conjSqrt_oneproof · cited by 1
- CFC.isStrictlyPositive_conjSqrt_iffproof · cited by 0