Theorems · Theorem · functional analysis
spectrum.star_mem_resolventSet_iff
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] [inst_3 : InvolutiveStar R]
[inst_4 : StarRing A] [StarModule R A] {r : R} {a : A}, star r ∈ resolventSet R a ↔ r ∈ resolventSet R (star a)- 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- StarRingstatement and proof · cited by 1,686
- IsUnitproof · cited by 1,602
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- star_starproof · cited by 135
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- InvolutiveStarstatement and proof · cited by 52
- StarModule.star_smulproof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- spectrum.map_starproof · cited by 0