Theorems · Theorem · functional analysis
star_left_conjugate_le_conjugate
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{a b : R}, a ≤ b → ∀ (c : R), star c * a * c ≤ star c * b * c- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.rangeproof · cited by 4,705
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- mul_addproof · cited by 413
- add_mulproof · cited by 363
- NonUnitalSemiringstatement and proof · cited by 339
- AddSubmonoid.closureproof · cited by 224
- star_left_conjugate_nonnegproof · cited by 6
- StarOrderedRing.le_iffproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.conjugate_le_conjugateproof · cited by 4
- star_left_conjugate_lt_conjugateproof · cited by 2
- IsStarProjection.mul_right_and_mul_left_of_nonneg_of_leproof · cited by 1
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- CStarAlgebra.nnnorm_sub_mul_self_leproof · cited by 1
- star_right_conjugate_le_conjugateproof · cited by 0