Theorems · Theorem · functional analysis
spectrum.mem_resolventSet_of_norm_lt_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} {k : 𝕜}, ‖a‖ * ‖1‖ < ‖k‖ → k ∈ resolventSet 𝕜 a- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- Unitsproof · cited by 2,804
- CompleteSpacestatement and proof · cited by 2,532
- Nontrivialproof · cited by 2,416
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- LT.lt.ne'proof · cited by 1,417
- NormedAlgebrastatement and proof · cited by 1,165
Cited by3
Results whose statement or proof uses this declaration.
- spectrum.norm_le_norm_mul_of_memproof · cited by 4
- spectrum.mem_resolventSet_of_norm_ltproof · cited by 1
- spectrum.eventually_isUnit_resolventproof · cited by 0