Theorems · Theorem · functional analysis
spectrum.isBounded
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] (a : A), Bornology.IsBounded (spectrum 𝕜 a)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 4 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- spectrumstatement · cited by 510
- Bornology.IsBoundedstatement · cited by 293
- Bornology.IsBounded.subsetproof · cited by 45
- Metric.isBounded_closedBallproof · cited by 19
- spectrum.subset_closedBall_norm_mulproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- spectrum.isCompactproof · cited by 5
- Subalgebra.spectrum_eq_of_isPreconnected_complproof · cited by 1
- Subalgebra.spectrum_isBounded_connectedComponentInproof · cited by 1
- IsSelfAdjoint.isConnected_spectrum_complproof · cited by 1