Theorems · Theorem · functional analysis
spectrum.coe_le_norm_of_mem
∀ {A : Type u_3} [inst : NormedRing A] [inst_1 : NormedAlgebra ℝ A] [CompleteSpace A] [NormOneClass A] {a : A}
{r : NNReal}, r ∈ spectrum NNReal a → ↑r ≤ ‖a‖- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 175 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
- Norm.normstatement · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- NNReal.toRealstatement · cited by 1,260
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormproof · cited by 952
- NormedRingstatement and proof · cited by 924
- spectrumstatement and proof · cited by 510
- NormOneClassstatement and proof · cited by 136
- NNReal.coe_monoproof · cited by 13
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