Theorems · Theorem · functional analysis

CStarModule.norm_eq_csSup

∀ {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] [inst_6 : CStarModule A E] [StarOrderedRing A] (v : E),
  ‖v‖ = sSup {x | ∃ w, ∃ (_ : ‖w‖ ≤ 1), ‖inner A w v‖ = x}

Defined in

Mathlib.Analysis.CStarAlgebra.Module.Defs

Cited by

0 results in Mathlib

Foundations

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

Assumes

NonUnitalCStarAlgebraPartialOrderAddCommGroupModuleSMulNormCStarModuleStarOrderedRing