Theorems · Theorem · functional analysis
IsometricContinuousFunctionalCalculus.spectrum_le
∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A] [inst_3 : PartialOrder A]
[StarOrderedRing A] [IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [NonnegSpectrumClass ℝ A] (a : A)
⦃x : NNReal⦄,
x ∈ spectrum NNReal a → autoParam (0 ≤ a) IsometricContinuousFunctionalCalculus.spectrum_le._auto_1 → x ≤ ‖a‖₊- Cited by
- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement and proof · cited by 952
- NormedRingstatement and proof · cited by 924
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- spectrumstatement and proof · cited by 510
- NonnegSpectrumClassstatement and proof · cited by 292
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