Mathlib Map

Theorems · Theorem · functional analysis

IsBoundedLinearMap.toIsLinearMap

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring 𝕜] [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : Module 𝕜 F] {f : E → F},
  IsBoundedLinearMap 𝕜 f → IsLinearMap 𝕜 f
Defined in
Mathlib.Analysis.Normed.Operator.BoundedLinearMaps
Cited by
7 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
SemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsBoundedLinearMap.neg · cited by 2IsBoundedLinearMap.negIsBoundedBilinearMap.map_sub_left · cited by 2IsBoundedBilinearMap.map_…IsBoundedBilinearMap.map_sub_right · cited by 2IsBoundedBilinearMap.map_…IsBoundedLinearMap.toLinearMap · cited by 0IsBoundedLinearMap.toLine…IsBoundedLinearMap.comp · cited by 0IsBoundedLinearMap.compIsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap · cited by 0IsBoundedLinearMap.isLine…IsBoundedLinearMap.lim_zero_bounded_linear_map · cited by 0IsBoundedLinearMap.lim_ze…isBoundedLinearMap_iff · cited by 0isBoundedLinearMap_iffModule · cited by 20661ModuleSemiring · cited by 13802SemiringSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupIsLinearMap · cited by 41IsLinearMapIsBoundedLinearMap · cited by 39IsBoundedLinearMapIsBoundedLinearMap.toIsLinear…CITED BYCITES

Cites5

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Cited by8

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