Theorems · Theorem · functional analysis
CStarAlgebra.increasingApproximateUnit
∀ (A : Type u_1) [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : StarOrderedRing A], (CStarAlgebra.approximateUnit A).IsIncreasingApproximateUnit
The filter CStarAlgebra.approximateUnit generated by the sections
{x | a ≤ x} ∩ closedBall 0 1 for 0 ≤ a forms an increasing approximate unit.
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- Foundations
- Depth 331 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- Norm.normproof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Metric.closedBallproof · cited by 704
- StarOrderedRingstatement and proof · cited by 587
- norm_zeroproof · cited by 366
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- dist_zero_rightproof · cited by 172
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Filter.Eventually.filter_monoproof · cited by 84
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