Theorems · Theorem · functional analysis
spectrum.units_smul_resolvent
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] {r : Rˣ} {s : R} {a : A},
r • resolvent a s = resolvent (r⁻¹ • a) (r⁻¹ • s)- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringRingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- smul_zeroproof · cited by 665
- spectrumproof · cited by 510
- IsUnit.unitproof · cited by 252
- Ring.inverseproof · cited by 160
Cited by1
Results whose statement or proof uses this declaration.
- spectrum.units_smul_resolvent_selfproof · cited by 1