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Theorems · Theorem · functional analysis

IsStarProjection.le_iff_mul_eq_left

∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {p q : A},
  IsStarProjection p → IsStarProjection q → (p ≤ q ↔ p * q = p)
Defined in
Mathlib.Analysis.CStarAlgebra.Projection
Cited by
1 results in Mathlib
Foundations
Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalCStarAlgebraPartialOrderStarOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsStarProjection.commute_of_le · cited by 0IsStarProjection.commute_…PartialOrder · cited by 6410PartialOrderStarOrderedRing · cited by 587StarOrderedRingIsIdempotentElem · cited by 217IsIdempotentElemList.TFAE.out · cited by 177TFAE.outNonUnitalCStarAlgebra · cited by 149NonUnitalCStarAlgebraIsStarProjection · cited by 64IsStarProjectionIsStarProjection.le_tfae · cited by 4IsStarProjection.le_tfaeIsStarProjection.le_iff_mul_e…CITED BYCITES

Cites7

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Cited by1

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