Theorems · Theorem · functional analysis

ContinuousLinearEquiv.hasSum

∀ {ι : Type u_5} {R : Type u_7} {R₂ : Type u_8} {M : Type u_9} {M₂ : Type u_10} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : AddCommMonoid M₂]
  [inst_5 : Module R₂ M₂] [inst_6 : TopologicalSpace M] [inst_7 : TopologicalSpace M₂] {σ : R →+* R₂} {σ' : R₂ →+* R}
  [inst_8 : RingHomInvPair σ σ'] [inst_9 : RingHomInvPair σ' σ] {L : SummationFilter ι} {f : ι → M} (e : M ≃SL[σ] M₂)
  {y : M₂}, HasSum (fun b => e (f b)) y L ↔ HasSum f (e.symm y) L

Applying a continuous linear map commutes with taking an (infinite) sum.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Module

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleAddCommMonoidModuleTopologicalSpaceTopologicalSpaceRingHomInvPairRingHomInvPair