Theorems · Definition · functional analysis

CStarModule.normedAddCommGroup

(A : Type u_1) →
  {E : Type u_2} →
    [inst : NonUnitalCStarAlgebra A] →
      [inst_1 : PartialOrder A] →
        [inst_2 : AddCommGroup E] →
          [inst_3 : Module ℂ E] →
            [inst_4 : SMul A E] → [inst_5 : Norm E] → [CStarModule A E] → [StarOrderedRing A] → NormedAddCommGroup E

This is not listed as an instance because we often want to replace the topology, uniformity and bornology instead of inheriting them from the norm.

Defined in

Mathlib.Analysis.CStarAlgebra.Module.Defs

Cited by

3 results in Mathlib

Foundations

Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCStarAlgebraPartialOrderAddCommGroupModuleSMulNormCStarModuleStarOrderedRing