Theorems · Definition · functional analysis

ContinuousLinearMap.smulRight

{M₁ : Type u_4} →
  [inst : TopologicalSpace M₁] →
    [inst_1 : AddCommMonoid M₁] →
      {M₂ : Type u_6} →
        [inst_2 : TopologicalSpace M₂] →
          [inst_3 : AddCommMonoid M₂] →
            {R : Type u_9} →
              {S : Type u_10} →
                [inst_4 : Semiring R] →
                  [inst_5 : Semiring S] →
                    [inst_6 : Module R M₁] →
                      [inst_7 : Module R M₂] →
                        [inst_8 : Module R S] →
                          [inst_9 : Module S M₂] →
                            [IsScalarTower R S M₂] →
                              [inst_11 : TopologicalSpace S] → [ContinuousSMul S M₂] → (M₁ →L[R] S) → M₂ → M₁ →L[R] M₂

The linear map fun x => c x • f. Associates to a scalar-valued linear map and an element of M₂ the M₂-valued linear map obtained by multiplying the two (a.k.a. tensoring by M₂). See also ContinuousLinearMap.smulRightₗ and ContinuousLinearMap.smulRightL.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

126 results in Mathlib

Foundations

Depth 76 from the axioms, rests on 941 definitions · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidSemiringSemiringModuleModuleModuleModuleIsScalarTowerTopologicalSpaceContinuousSMul