Theorems · Theorem · functional analysis
isStarProjection_iff_isIdempotentElem_and_isStarNormal
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : NonUnitalRing A] [inst_2 : StarRing A] [inst_3 : Module ℂ A]
[inst_4 : IsScalarTower ℂ A A] [inst_5 : SMulCommClass ℂ A A] [NonUnitalContinuousFunctionalCalculus ℂ A IsStarNormal]
{p : A}, IsStarProjection p ↔ IsIdempotentElem p ∧ IsStarNormal pAn element in a non-unital C⋆-algebra is a star projection if and only if it is idempotent and normal.
- Defined in
- Mathlib.Analysis.CStarAlgebra.Projection
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Complexstatement and proof · cited by 5,565
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- NonUnitalRingstatement and proof · cited by 422
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
- IsIdempotentElemstatement and proof · cited by 217
- IsStarNormalstatement and proof · cited by 117
- IsStarProjectionstatement · cited by 64
- Iff.eqproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- isStarProjection_iff_quasispectrum_subset_and_isStarNormalproof · cited by 0
- isStarProjection_iff_spectrum_subset_and_isStarNormalproof · cited by 0