Theorems · Theorem · functional analysis
CStarAlgebra.exists_sum_four_unitary
∀ {A : Type u_1} [inst : CStarAlgebra A] (x : A), ∃ u c, x = ∑ i, c i • ↑(u i) ∧ ∀ (i : Fin 4), ‖c i‖ ≤ ‖x‖ / 2Every element x in a unital C⋆-algebra is a linear combination of four unitary elements,
and the norm of each coefficient does not exceed ‖x‖ / 2.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 327 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.span_unitaryproof · cited by 0