Theorems · Definition · functional analysis

ContinuousMultilinearMap.toMultilinearMapLinear

{ι : Type v} →
  {M₁ : ι → Type w₁} →
    {M₂ : Type w₂} →
      {R' : Type u_1} →
        {A : Type u_2} →
          [inst : Semiring R'] →
            [inst_1 : Semiring A] →
              [inst_2 : (i : ι) → AddCommMonoid (M₁ i)] →
                [inst_3 : AddCommMonoid M₂] →
                  [inst_4 : (i : ι) → TopologicalSpace (M₁ i)] →
                    [inst_5 : TopologicalSpace M₂] →
                      [inst_6 : ContinuousAdd M₂] →
                        [inst_7 : (i : ι) → Module A (M₁ i)] →
                          [inst_8 : Module A M₂] →
                            [inst_9 : Module R' M₂] →
                              [inst_10 : ContinuousConstSMul R' M₂] →
                                [inst_11 : SMulCommClass A R' M₂] →
                                  ContinuousMultilinearMap A M₁ M₂ →ₗ[R'] MultilinearMap A M₁ M₂

Linear map version of the map toMultilinearMap associating to a continuous multilinear map the corresponding multilinear map.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidTopologicalSpaceTopologicalSpaceContinuousAddModuleModuleModuleContinuousConstSMulSMulCommClass