Theorems · Theorem · functional analysis
quasispectrum.isCompact
∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] {B : Type u_3} [inst_1 : NonUnitalNormedRing B] [inst_2 : NormedSpace 𝕜 B]
[CompleteSpace B] [IsScalarTower 𝕜 B B] [SMulCommClass 𝕜 B B] [ProperSpace 𝕜] (a : B), IsCompact (quasispectrum 𝕜 a)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- NormedSpacestatement and proof · cited by 12,499
- IsScalarTowerstatement and proof · cited by 3,896
- CompleteSpacestatement and proof · cited by 2,532
- SMulCommClassstatement and proof · cited by 1,927
- IsCompactstatement and proof · cited by 1,282
- NormedFieldstatement and proof · cited by 1,084
- AlgEquiv.symmproof · cited by 615
- quasispectrumstatement · cited by 292
- NonUnitalNormedRingstatement and proof · cited by 231
- ProperSpacestatement and proof · cited by 190
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousOn.cfcₙ_of_mem_nhdsSetproof · cited by 1
- CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁proof · cited by 0
- CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₁₂proof · cited by 0