Theorems · Theorem · functional analysis

Seminorm.const_isBounded

∀ {𝕜 : Type u_2} {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} {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} [inst_6 : RingHomIsometric σ₁₂] (ι : Type u_11) [Nonempty ι]
  {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} (f : E →ₛₗ[σ₁₂] F),
  Seminorm.IsBounded (fun x => p) q f ↔ ∀ (i : ι'), ∃ C, (q i).comp f ≤ C • p

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupModuleSeminormedRingAddCommGroupModuleRingHomIsometricNonempty