Theorems · Theorem · functional analysis
CStarAlgebra.isUnit_of_le
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] (a : A) {b : A},
a ≤ b → autoParam (IsStrictlyPositive a) CStarAlgebra.isUnit_of_le._auto_1 → IsUnit bIn a unital C⋆-algebra, if a is strictly positive, and a ≤ b, then b is
invertible.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- Nontrivialproof · cited by 2,416
- IsUnitstatement · cited by 1,602
- StarOrderedRingstatement and proof · cited by 587
- spectrumproof · cited by 510
- CStarAlgebrastatement and proof · cited by 123
- not_le_of_gtproof · cited by 97
- IsStrictlyPositivestatement and proof · cited by 75
Cited by3
Results whose statement or proof uses this declaration.
- IsStrictlyPositive.of_leproof · cited by 4
- CStarAlgebra.rpow_neg_one_le_rpow_neg_oneproof · cited by 1
- CStarAlgebra.rpow_neg_one_le_oneproof · cited by 0