Theorems · Theorem · functional analysis
CStarAlgebra.exists_sum_four_nonneg
∀ {A : Type u_2} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] (a : A),
∃ x, (∀ (i : Fin 4), 0 ≤ x i) ∧ (∀ (i : Fin 4), ‖x i‖ ≤ ‖a‖) ∧ a = ∑ i, Complex.I ^ ↑i • x i- Cited by
- 1 results in Mathlib
- Foundations
- Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Algebra.algebraMapproof · cited by 4,706
- Finset.univstatement and proof · cited by 3,473
- LE.le.transproof · cited by 3,151
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
Cited by1
Results whose statement or proof uses this declaration.
- PositiveLinearMap.exists_norm_apply_leproof · cited by 0