Theorems · Definition · functional analysis

LinearMap.polar

{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] → (E →ₗ[𝕜] F →ₗ[𝕜] 𝕜) → Set E → Set F

The (absolute) polar of s : Set E is given by the set of all y : F such that ‖B x y‖ ≤ 1 for all x ∈ s.

Defined in

Mathlib.Analysis.LocallyConvex.Polar

Cited by

23 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedCommRingAddCommMonoidAddCommMonoidModuleModule