Theorems · Theorem · functional analysis
spectrum.subset_closedBall_norm_mul
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] (a : A), spectrum 𝕜 a ⊆ Metric.closedBall 0 (‖a‖ * ‖1‖)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NormedRingstatement and proof · cited by 924
- Metric.closedBallstatement · cited by 704
- spectrumstatement and proof · cited by 510
- dist_zero_rightproof · cited by 172
- spectrum.norm_le_norm_mul_of_memproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- upperHemicontinuous_spectrumproof · cited by 4
- spectrum.isBoundedproof · cited by 4