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Theorems · Definition · functional analysis

WithCStarModule.equivL

(R : Type u_1) →
  {A : Type u_3} →
    {E : Type u_4} →
      [inst : Semiring R] →
        [inst_1 : AddCommGroup E] → [inst_2 : UniformSpace E] → [inst_3 : Module R E] → WithCStarModule A E ≃L[R] E

WithCStarModule.equiv as a continuous linear equivalence between C⋆ᵐᵒᵈ E and E.

Defined in
Mathlib.Analysis.CStarAlgebra.Module.Synonym
Cited by
2 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommGroupUniformSpaceModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CStarMatrix.toCLM · cited by 13CStarMatrix.toCLMWithCStarModule.equivL_apply · cited by 0WithCStarModule.equivL_ap…WithCStarModule.equivL_symm_apply · cited by 0WithCStarModule.equivL_sy…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommGroup · cited by 12871AddCommGroupLinearEquiv · cited by 3317LinearEquivUniformSpace · cited by 2040UniformSpaceContinuousLinearEquiv · cited by 743ContinuousLinearEquivWithCStarModule · cited by 66WithCStarModuleWithCStarModule.linearEquiv · cited by 3WithCStarModule.linearEqu…WithCStarModule.equivLCITED BYCITES

Cites9

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Cited by3

Results whose statement or proof uses this declaration.