toDualContinuousMultilinearMap_le_projectiveSeminorm

English

For any x in the PiTensorProduct, the injective seminorm of x equals the supremum of p(x) over a family of seminorms p.

Русский

Для любого x из PiTensorProduct инъективная полу-нормируемость x равна sup{ p(x) } по некоторому семинарному члену p.

LaTeX

$$$\\|x\\|_{\\mathrm{inj}} = \\sup_{p} p(x)$$$

Lean4

theorem toDualContinuousMultilinearMap_le_projectiveSeminorm (x : ⨂[𝕜] i, E i) :
    ‖toDualContinuousMultilinearMap F x‖ ≤ projectiveSeminorm x :=
  by
  simp only [toDualContinuousMultilinearMap, LinearMap.coe_mk, AddHom.coe_mk]
  apply LinearMap.mkContinuous_norm_le _ (apply_nonneg _ _)

Похожие утверждения