Theorems · Theorem · functional analysis
CStarAlgebra.span_nonneg_inter_unitBall
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A],
Submodule.span ℂ ({x | 0 ≤ x} ∩ Metric.ball 0 1) = ⊤A C⋆-algebra is spanned by nonnegative strict contractions.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 316 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredstatement · cited by 6,101
- Complexstatement · cited by 5,565
- Submodule.spanstatement · cited by 1,504
- Metric.ballstatement · cited by 735
- zero_lt_oneproof · cited by 598
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalCStarAlgebrastatement and proof · cited by 149
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.tendsto_mul_right_of_forall_nonneg_tendstoproof · cited by 0