Theorems · Definition · functional analysis

Seminorm.IsBounded

{𝕜 : Type u_2} →
  {𝕜₂ : Type u_3} →
    {E : Type u_6} →
      {F : Type u_7} →
        {ι : Type u_9} →
          {ι' : Type u_10} →
            [inst : SeminormedRing 𝕜] →
              [inst_1 : AddCommGroup E] →
                [inst_2 : Module 𝕜 E] →
                  [inst_3 : SeminormedRing 𝕜₂] →
                    [inst_4 : AddCommGroup F] →
                      [inst_5 : Module 𝕜₂ F] →
                        {σ₁₂ : 𝕜 →+* 𝕜₂} →
                          [RingHomIsometric σ₁₂] → (ι → Seminorm 𝕜 E) → (ι' → Seminorm 𝕜₂ F) → (E →ₛₗ[σ₁₂] F) → Prop

The proposition that a linear map is bounded between spaces with families of seminorms.

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

7 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupModuleSeminormedRingAddCommGroupModuleRingHomIsometric