Theorems · Theorem · functional analysis

CStarAlgebra.isBasis_nonneg_sections

∀ (A : Type u_1) [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A],
  Filter.IsBasis (fun x => 0 ≤ x ∧ ‖x‖ < 1) fun x => {x_1 | x ≤ x_1}

The sections of positive strict contractions form a filter basis.

Defined in

Mathlib.Analysis.CStarAlgebra.ApproximateUnit

Cited by

2 results in Mathlib

Foundations

Depth 327 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCStarAlgebraPartialOrderStarOrderedRing