isBoundedBilinearMap_smulRight — Mathlib

English

In any Mul instance, the product a b equals the scalar multiplication a • b.

Русский

Во всех кольцах/полях умножение a b совпадает с действием скаляра a на b: a · b = a b.

LaTeX

$$$\forall a,b,\ a \cdot b = a \star b$$$

Lean4

/-- The function `ContinuousLinearMap.smulRight`, associating to a continuous linear map
`f : E → 𝕜` and a scalar `c : F` the tensor product `f ⊗ c` as a continuous linear map from `E` to
`F`, is a bounded bilinear map. -/
theorem isBoundedBilinearMap_smulRight :
    IsBoundedBilinearMap 𝕜 fun p => (ContinuousLinearMap.smulRight : StrongDual 𝕜 E → F → E →L[𝕜] F) p.1 p.2 :=
  (smulRightL 𝕜 E F).isBoundedBilinearMap

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