diff 9506729..b1f9bc4 tracial_property_gamma_v2.txt
diff --git a/tracial_property_gamma_v2.txt b/tracial_property_gamma_v2.txt index 866352a..1612c6a 100644 --- a/tracial_property_gamma_v2.txt +++ b/tracial_property_gamma_v2.txt @@ -47,41 +47,7 @@ be manufactured out of positive elements. The printed source combines them; here every part is completely self-contained, importing only Section 1 from outside itself. -Reading guide -------------- - -Section 1 fixes notation once. Do not skip it. - -Part I (Sections 2 - 5) proves Route 1. -Part II (Sections 6 -10) proves Route 2. -Part III(Sections 11-15) proves Route 3. - -Every lemma is proved at its point of first use. Every external -theorem is quoted in full at the point where the proof invokes it. -When a hypothesis enters, the proof says which one. - -A reader who wants only the unital Toms-Winter direction may read -Section 1, then Part II. Lemma 7.1 in Part II uses Lemma 2.2 from -Part I; Lemma 2.2 requires no real rank zero and no nuclearity, so -this reuse is safe and is flagged at the point of use. - -A note on rigor. Each use of each hypothesis is flagged. Where an -estimate is made we show the chain of inequalities; where something -is genuinely routine (a triangle inequality on finitely many terms, -a telescoping sum) we say so and do it. No step is left as an -exercise unless the exercise is truly instantaneous. - -A note on notation. We keep the same letters across all three parts: -A is the algebra under study; T is its tracial state space; tau, -sigma, rho, nu, lambda are specific traces; omega is a free -ultrafilter on N; D is the ultrapower in which central projections -live; Lambda is the designated family of limit traces on D. -Parts I and II have a unital A and a unital D; Part III builds a -unital D from a nonunital A. The sentence "Now D is...", at the -head of each part, fixes the meaning of D for that part. - -=========================================================================== - SECTION 1. Conventions +SECTION 1. Conventions =========================================================================== Throughout, A is a separable C*-algebra. A C*-algebra is unital