Theorems · Definition · functional analysis

ContinuousLinearMap.restrictScalars

{A : Type u_1} →
  {M₁ : Type u_2} →
    {M₂ : Type u_3} →
      (R : Type u_4) →
        [inst : Semiring A] →
          [inst_1 : Semiring R] →
            [inst_2 : AddCommMonoid M₁] →
              [inst_3 : Module A M₁] →
                [inst_4 : Module R M₁] →
                  [inst_5 : TopologicalSpace M₁] →
                    [inst_6 : AddCommMonoid M₂] →
                      [inst_7 : Module A M₂] →
                        [inst_8 : Module R M₂] →
                          [inst_9 : TopologicalSpace M₂] →
                            [LinearMap.CompatibleSMul M₁ M₂ R A] → (M₁ →L[A] M₂) → M₁ →L[R] M₂

If A is an R-algebra, then a continuous A-linear map can be interpreted as a continuous R-linear map. We assume LinearMap.CompatibleSMul M₁ M₂ R A to match assumptions of LinearMap.map_smul_of_tower.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.RestrictScalars

Cited by

61 results in Mathlib

Foundations

Depth 25 from the axioms · uses no axioms

Assumes

SemiringSemiringAddCommMonoidModuleModuleTopologicalSpaceAddCommMonoidModuleModuleTopologicalSpaceLinearMap.CompatibleSMul