Theorems · Theorem · functional analysis
spectrum.isCompact
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] [ProperSpace 𝕜] (a : A), IsCompact (spectrum 𝕜 a)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsCompactstatement · cited by 1,282
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NormedRingstatement and proof · cited by 924
- spectrumstatement · cited by 510
- ProperSpacestatement and proof · cited by 190
- Metric.isCompact_of_isClosed_isBoundedproof · cited by 8
- spectrum.isBoundedproof · cited by 4
- spectrum.isClosedproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- quasispectrum.isCompactproof · cited by 3
- spectrum.exists_nnnorm_eq_spectralRadius_of_nonemptyproof · cited by 3
- ContinuousOn.cfc_of_mem_nhdsSetproof · cited by 2
- spectrum.spectralRadius_lt_of_forall_lt_of_nonemptyproof · cited by 1
- Unitary.norm_sub_one_lt_two_iffproof · cited by 1