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Theorems · Definition · functional analysis

WithCStarModule.linearEquiv

(R : Type u_1) →
  (A : Type u_3) →
    (E : Type u_4) →
      [inst : Semiring R] → [inst_1 : AddCommGroup E] → [inst_2 : Module R E] → WithCStarModule A E ≃ₗ[R] E

WithCStarModule.equiv as a linear equivalence.

Defined in
Mathlib.Analysis.CStarAlgebra.Module.Synonym
Cited by
3 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithCStarModule.equivL · cited by 2WithCStarModule.equivLWithCStarModule.linearEquiv_apply · cited by 0WithCStarModule.linearEqu…WithCStarModule.linearEquiv_symm_apply · cited by 0WithCStarModule.linearEqu…WithCStarModule.map_top_submodule · cited by 0WithCStarModule.map_top_s…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommGroup · cited by 12871AddCommGroupEquiv.symm · cited by 3681Equiv.symmLinearEquiv · cited by 3317LinearEquivLinearEquiv.refl · cited by 143LinearEquiv.reflWithCStarModule · cited by 66WithCStarModuleWithCStarModule.equiv · cited by 33WithCStarModule.equivWithCStarModule.linearEquivCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.