Theorems · Theorem · functional analysis
CStarModule.normedSpaceCore
∀ (A : Type u_1) {E : Type u_2} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : AddCommGroup E]
[inst_3 : Module ℂ E] [inst_4 : SMul A E] [inst_5 : Norm E] [CStarModule A E] [StarOrderedRing A],
NormedSpace.Core ℂ EThis allows us to get NormedAddCommGroup and NormedSpace instances on E via
NormedAddCommGroup.ofCore and NormedSpace.ofCore.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 323 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- StarRingproof · cited by 1,686
- Inner.innerproof · cited by 1,089
- starRingEndproof · cited by 671
- StarOrderedRingstatement and proof · cited by 587
- Real.sqrtproof · cited by 545
- Normstatement and proof · cited by 512
Cited by2
Results whose statement or proof uses this declaration.
- CStarModule.normedAddCommGroupproof · cited by 3
- CStarModule.norm_eq_csSupproof · cited by 0