Theorems · Theorem · functional analysis
DoubleCentralizer.norm_fst
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NonUnitalNormedRing A]
[inst_2 : NormedSpace 𝕜 A] [inst_3 : SMulCommClass 𝕜 A A] [inst_4 : IsScalarTower 𝕜 A A] [inst_5 : StarRing A]
[CStarRing A] (a : DoubleCentralizer 𝕜 A), ‖a.toProd.1‖ = ‖a‖- Defined in
- Mathlib.Analysis.CStarAlgebra.Multiplier
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- LinearOrderproof · cited by 8,572
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- le_rflproof · cited by 1,558
- NonUnitalNormedRingstatement and proof · cited by 231
Cited by2
Results whose statement or proof uses this declaration.
- DoubleCentralizer.norm_sndproof · cited by 1
- DoubleCentralizer.nnnorm_fstproof · cited by 0