Theorems · Theorem · operator theory
ContinuousLinearMap.IsPositive.add
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{T S : E →L[𝕜] E}, T.IsPositive → S.IsPositive → (T + S).IsPositive- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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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.IsPositivestatement and proof · cited by 38
- ContinuousLinearMap.isPositive_toLinearMap_iffproof · cited by 7
- ContinuousLinearMap.IsPositive.toLinearMapproof · cited by 6
- LinearMap.IsPositive.addproof · cited by 1
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