Theorems · Theorem · functional analysis
IsStarProjection.le_iff_idempotent_sub
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {p q : A},
IsStarProjection p → IsStarProjection q → (p ≤ q ↔ IsIdempotentElem (q - p))- Defined in
- Mathlib.Analysis.CStarAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- StarOrderedRingstatement and proof · cited by 587
- IsIdempotentElemstatement and proof · cited by 217
- List.TFAE.outproof · cited by 177
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- IsStarProjectionstatement and proof · cited by 64
- IsStarProjection.le_tfaeproof · cited by 4
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