Theorems · Theorem · functional analysis
IsSelfAdjoint.nnnorm_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
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- StarRingstatement and proof · cited by 1,686
- NNNorm.nnnormstatement · cited by 952
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalNormedRingstatement and proof · cited by 231
- CStarRingstatement and proof · cited by 61
- IsSelfAdjoint.norm_mul_selfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.nnnorm_pow_two_powproof · cited by 2