Theorems · Theorem · functional analysis

LinearMap.polar_mem_iff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedCommRing 𝕜] [inst_1 : AddCommMonoid E]
  [inst_2 : AddCommMonoid F] [inst_3 : Module 𝕜 E] [inst_4 : Module 𝕜 F] (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜) (s : Set E) (y : F),
  y ∈ B.polar s ↔ ∀ x ∈ s, ‖(B x) y‖ ≤ 1

Defined in

Mathlib.Analysis.LocallyConvex.Polar

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedCommRingAddCommMonoidAddCommMonoidModuleModule