Theorems · Theorem · functional analysis
spectrum.resolvent_isBigO_inv
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] (a : A), resolvent a =O[Bornology.cobounded 𝕜] Inv.inv- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- Norm.normproof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Filter.Tendstoproof · cited by 3,814
- Compl.complproof · cited by 2,925
- Unitsproof · cited by 2,804
- CompleteSpacestatement and proof · cited by 2,532
- Units.valproof · cited by 1,966
- Filter.univ_mem'proof · cited by 1,672
Cited by1
Results whose statement or proof uses this declaration.
- spectrum.resolvent_tendsto_coboundedproof · cited by 1