toSeminormFamily_apply — Mathlib

English

A weak bilinear seminorm linearizes a bilinear form B into a seminorm on a function space via y ↦ (B.flip y).toSeminorm.

Русский

Слабая билинейная полупринормальная величина переводит билину в полуnorm через y ↦ (B.flip y).toSeminorm.

LaTeX

$$$\text{weakBilin_withSeminorms}(B) : WithSeminorms(B.toSeminormFamily)$$$

Lean4

@[simp]
theorem toSeminormFamily_apply {B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜} {x y} : (B.toSeminormFamily y) x = ‖B x y‖ :=
  rfl

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