Theorems · Definition · functional analysis

WithCStarModule.normedAddCommGroupProdAux

{A : Type u_1} →
  [inst : NonUnitalCStarAlgebra A] →
    [inst_1 : PartialOrder A] →
      {E : Type u_2} →
        {F : Type u_3} →
          [inst_2 : NormedAddCommGroup E] →
            [inst_3 : Module ℂ E] →
              [inst_4 : SMul A E] →
                [inst_5 : NormedAddCommGroup F] →
                  [inst_6 : Module ℂ F] →
                    [inst_7 : SMul A F] →
                      [CStarModule A E] →
                        [CStarModule A F] → [StarOrderedRing A] → NormedAddCommGroup (WithCStarModule A (E × F))

A normed additive commutative group structure on C⋆ᵐᵒᵈ(A, E × F) with the wrong topology, uniformity and bornology. This is only used to build the instance with the correct forgetful inheritance data.

Defined in

Mathlib.Analysis.CStarAlgebra.Module.Constructions

Cited by

0 results in Mathlib

Foundations

Depth 325 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCStarAlgebraPartialOrderNormedAddCommGroupModuleSMulNormedAddCommGroupModuleSMulCStarModuleCStarModuleStarOrderedRing