Theorems · Theorem · functional analysis
isStarProjection_iff_spectrum_subset_and_isStarNormal
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[NonUnitalContinuousFunctionalCalculus ℂ A IsStarNormal] {p : A},
IsStarProjection p ↔ spectrum ℂ p ⊆ {0, 1} ∧ IsStarNormal p- Defined in
- Mathlib.Analysis.CStarAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- StarRingstatement and proof · cited by 1,686
- spectrumstatement · cited by 510
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
- IsStarNormalstatement and proof · cited by 117
- IsStarProjectionstatement · cited by 64
- Iff.eqproof · cited by 14
- isIdempotentElem_iff_spectrum_subsetproof · cited by 2
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