Theorems · Theorem · functional analysis

LinearIsometryEquiv.piLpCongrLeft_single

∀ {p : ENNReal} {𝕜 : Type u_1} {ι : Type u_2} [hp : Fact (1 ≤ p)] [inst : Fintype ι] [inst_1 : Semiring 𝕜]
  {ι' : Type u_5} [inst_2 : Fintype ι'] {E : Type u_6} [inst_3 : SeminormedAddCommGroup E] [inst_4 : Module 𝕜 E]
  [inst_5 : DecidableEq ι] [inst_6 : DecidableEq ι'] (e : ι ≃ ι') (i : ι) (v : E),
  (LinearIsometryEquiv.piLpCongrLeft p 𝕜 E e) (PiLp.single p i v) = PiLp.single p (e i) v

Defined in

Mathlib.Analysis.Normed.Lp.PiLp

Cited by

2 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactFintypeSemiringFintypeSeminormedAddCommGroupModuleDecidableEqDecidableEq