Theorems · Theorem · functional analysis
IsStarProjection.le_tfae
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {p q : A},
IsStarProjection p →
IsStarProjection q → [p ≤ q, q * p = p, p * q = p, IsStarProjection (q - p), IsIdempotentElem (q - p)].TFAE- Defined in
- Mathlib.Analysis.CStarAlgebra.Projection
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Star.starproof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- IsIdempotentElemstatement and proof · cited by 217
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- List.TFAEstatement · cited by 102
- List.tfae_of_cycleproof · cited by 83
- StarMul.star_mulproof · cited by 72
- IsStarProjectionstatement and proof · cited by 64
- IsSelfAdjoint.star_eqproof · cited by 58
- IsStarProjection.isSelfAdjointproof · cited by 18
- IsSelfAdjoint.subproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- IsStarProjection.le_iff_mul_eq_leftproof · cited by 1
- IsStarProjection.le_iff_mul_eq_rightproof · cited by 1
- IsStarProjection.le_iff_subproof · cited by 0
- IsStarProjection.le_iff_idempotent_subproof · cited by 0