Theorems · Theorem · functional analysis

selfAdjointPartL_apply_coe

∀ (R : Type u_1) (A : Type u_2) [inst : Semiring R] [inst_1 : StarMul R] [inst_2 : TrivialStar R]
  [inst_3 : AddCommGroup A] [inst_4 : Module R A] [inst_5 : StarAddMonoid A] [inst_6 : StarModule R A]
  [inst_7 : Invertible 2] [inst_8 : TopologicalSpace A] [inst_9 : ContinuousAdd A] [inst_10 : ContinuousStar A]
  [inst_11 : ContinuousConstSMul R A] (x : A), ↑((selfAdjointPartL R A) x) = ⅟2 • x + ⅟2 • star x

Defined in

Mathlib.Topology.Algebra.Module.Star

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringStarMulTrivialStarAddCommGroupModuleStarAddMonoidStarModuleInvertibleTopologicalSpaceContinuousAddContinuousStarContinuousConstSMul