Theorems · Theorem · functional analysis
isStarProjection_iff_spectrum_subset_and_isSelfAdjoint
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℝ A]
[NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] {p : A},
IsStarProjection p ↔ spectrum ℝ p ⊆ {0, 1} ∧ IsSelfAdjoint p- Defined in
- Mathlib.Analysis.CStarAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- StarRingstatement and proof · cited by 1,686
- IsSelfAdjointstatement and proof · cited by 545
- spectrumstatement · cited by 510
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
- IsStarProjectionstatement · cited by 64
- Iff.eqproof · cited by 14
- isStarProjection_iffproof · cited by 6
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