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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
Defined in
Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart
Cited by
1 results in Mathlib
Foundations
Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalCStarAlgebraPartialOrderStarOrderedRing

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