Theorems · Definition · functional analysis

ContinuousLinearMap.lsmul

(𝕜 : Type u_1) →
  {E : Type u_2} →
    [inst : NontriviallyNormedField 𝕜] →
      [inst_1 : SeminormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          (R : Type u_3) →
            [inst_3 : SeminormedRing R] →
              [inst_4 : NormedAlgebra 𝕜 R] →
                [inst_5 : Module R E] → [IsBoundedSMul R E] → [IsScalarTower 𝕜 R E] → R →L[𝕜] E →L[𝕜] E

Scalar multiplication as a continuous bilinear map.

Defined in

Mathlib.Analysis.Normed.Operator.Mul

Cited by

66 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedRingNormedAlgebraModuleIsBoundedSMulIsScalarTower