Theorems · Theorem · functional analysis
selfAdjoint.star_coe_unitarySelfAddISMul
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : StarOrderedRing A] (a : ↥(selfAdjoint A))
(ha_norm : ‖a‖ ≤ 1), star ↑(selfAdjoint.unitarySelfAddISMul a ha_norm) = ↑a - Complex.I • CFC.sqrt (1 - ↑a ^ 2)- Cited by
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- Foundations
- Depth 325 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- Submonoidstatement · cited by 3,086
- Star.starstatement and proof · cited by 1,082
- Complex.Istatement and proof · cited by 866
- StarOrderedRingstatement and proof · cited by 587
- neg_smulproof · cited by 306
- unitarystatement · cited by 207
- selfAdjointstatement and proof · cited by 135
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