Theorems · Theorem · functional analysis

Seminorm.IsBounded.of_real

∀ {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} [inst_6 : RingHomIsometric σ₁₂] {p : ι → Seminorm 𝕜 E}
  {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F},
  (∀ (i : ι'), ∃ s C, ∀ (x : E), (q i) (f x) ≤ C * (s.sup p) x) → Seminorm.IsBounded p q f

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

0 results in Mathlib

Foundations

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

Assumes

SeminormedRingAddCommGroupModuleSeminormedRingAddCommGroupModuleRingHomIsometric