Theorems · Definition · functional analysis

selfAdjointPartL

(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] →
                  [Invertible 2] →
                    [inst_8 : TopologicalSpace A] →
                      [ContinuousAdd A] → [ContinuousStar A] → [ContinuousConstSMul R A] → A →L[R] ↥(selfAdjoint A)

The self-adjoint part of an element of a star module, as a continuous linear map.

Defined in

Mathlib.Topology.Algebra.Module.Star

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringStarMulTrivialStarAddCommGroupModuleStarAddMonoidStarModuleInvertibleTopologicalSpaceContinuousAddContinuousStarContinuousConstSMul