Theorems · Theorem · functional analysis
IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum
∀ {𝕜 : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} [inst : RCLike 𝕜] [inst_1 : NormedRing A]
[inst_2 : StarRing A] [inst_3 : NormedAlgebra 𝕜 A] [IsometricContinuousFunctionalCalculus 𝕜 A p] [Nontrivial A]
(a : A),
autoParam (p a) IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum._auto_1 →
IsGreatest ((fun x => ‖x‖) '' spectrum 𝕜 a) ‖a‖- Cited by
- 0 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.imagestatement and proof · cited by 5,609
- Norm.normstatement and proof · cited by 5,413
- RCLikestatement and proof · cited by 2,829
- Nontrivialstatement and proof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- spectrumstatement and proof · cited by 510
- IsGreateststatement and proof · cited by 112
- continuousOn_id'proof · cited by 109
- IsometricContinuousFunctionalCalculusstatement and proof · cited by 62
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