Theorems · Theorem · functional analysis
spectrum.le_nnnorm_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
- 2 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- NNReal.toRealproof · cited by 1,260
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement · cited by 952
- NormedRingstatement and proof · cited by 924
- spectrumstatement and proof · cited by 510
- NormOneClassstatement and proof · cited by 136
- Real.le_norm_selfproof · cited by 16
- spectrum.norm_le_norm_of_memproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.le_nnnorm_of_mem_quasispectrumproof · cited by 1
- spectrum.coe_le_norm_of_memproof · cited by 0