Theorems · Theorem · functional analysis
IsSelfAdjoint.norm_mul_self
∀ {E : Type u_2} [inst : NonUnitalNormedRing E] [inst_1 : StarRing E] [CStarRing E] {x : E},
IsSelfAdjoint x → ‖x * x‖ = ‖x‖ ^ 2- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 119 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.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- StarRingstatement and proof · cited by 1,686
- IsSelfAdjointstatement and proof · cited by 545
- sqproof · cited by 280
- NonUnitalNormedRingstatement and proof · cited by 231
- CStarRingstatement and proof · cited by 61
- IsSelfAdjoint.star_eqproof · cited by 58
- CStarRing.norm_star_mul_selfproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.nnnorm_mul_selfproof · cited by 1
- IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitaryproof · cited by 0