Theorems · Theorem · functional analysis
Unitization.norm_inr
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NonUnitalNormedRing A]
[inst_2 : NormedSpace 𝕜 A] [inst_3 : IsScalarTower 𝕜 A A] [inst_4 : SMulCommClass 𝕜 A A]
[inst_5 : RegularNormedAlgebra 𝕜 A] (a : A), ‖↑a‖ = ‖a‖- Cited by
- 8 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idproof · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapproof · cited by 5,352
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- zero_addproof · cited by 2,366
- SMulCommClassstatement and proof · cited by 1,927
- map_zeroproof · cited by 1,614
Cited by8
Results whose statement or proof uses this declaration.
- Unitization.isometry_inrproof · cited by 7
- CStarAlgebra.norm_le_norm_of_nonneg_of_leproof · cited by 6
- NonUnitalStarAlgHom.norm_mapproof · cited by 2
- Unitization.nnnorm_inrproof · cited by 2
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- CStarAlgebra.inr_mem_Icc_iff_norm_leproof · cited by 1
- CStarAlgebra.norm_sub_mul_self_le_of_inrproof · cited by 0