Theorems · Definition · functional analysis

StarModule.decomposeProdAdjointL

(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] →
                      [IsTopologicalAddGroup A] →
                        [ContinuousStar A] → [ContinuousConstSMul R A] → A ≃L[R] ↥(selfAdjoint A) × ↥(skewAdjoint A)

The decomposition of elements of a star module into their self- and skew-adjoint parts, as a continuous linear equivalence.

Defined in

Mathlib.Topology.Algebra.Module.Star

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringStarMulTrivialStarAddCommGroupModuleStarAddMonoidStarModuleInvertibleTopologicalSpaceIsTopologicalAddGroupContinuousStarContinuousConstSMul