Theorems · Theorem · functional analysis

spectrum.hasDerivAt_resolvent_const_right

∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField A]
  [inst_2 : NormedAlgebra 𝕜 A] [CompleteSpace A] {a : A} {k : 𝕜},
  k ∈ resolventSet 𝕜 a → HasDerivAt (fun x => resolvent x k) (resolvent a k ^ 2) a

Defined in

Mathlib.Analysis.Normed.Algebra.GelfandFormula

Cited by

1 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebraCompleteSpace