Theorems · Theorem · operator theory
ContinuousLinearMap.IsPositive.toLinearMap
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(T : E →L[𝕜] E), T.IsPositive → (↑T).IsPositiveAlias of the reverse direction of ContinuousLinearMap.isPositive_toLinearMap_iff.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- ContinuousLinearMap.toLinearMapstatement · cited by 528
- LinearMap.IsPositivestatement · cited by 39
- ContinuousLinearMap.IsPositivestatement · cited by 38
- ContinuousLinearMap.isPositive_toLinearMap_iffproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.IsPositive.inner_nonneg_rightproof · cited by 2
- ContinuousLinearMap.isPositive_iff_eq_sum_rankOneproof · cited by 1
- ContinuousLinearMap.IsPositive.re_inner_nonneg_rightproof · cited by 0
- ContinuousLinearMap.IsPositive.smul_of_nonnegproof · cited by 0
- ContinuousLinearMap.IsPositive.addproof · cited by 0
- ContinuousLinearMap.IsPositive.inner_nonneg_leftproof · cited by 0