Theorems · Theorem · operator theory
ContinuousLinearMap.isPositive_self_comp_adjoint
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
[inst_5 : CompleteSpace E] [inst_6 : CompleteSpace F] (S : E →L[𝕜] F),
(S ∘SL ContinuousLinearMap.adjoint S).IsPositive- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- LinearIsometryEquivstatement · cited by 748
- ContinuousLinearMap.compstatement · cited by 709
- starRingEndstatement · cited by 671
- ContinuousLinearMap.adjointstatement · cited by 82
- ContinuousLinearMap.IsPositivestatement · cited by 38
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