2000/09/06 by Gilles Pisier, Pisier, Gilles
Mathematics · #46 K 99 #46 L 07 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:07 #msc:46 #msc:99
paper · pdf · doi:10.48550/arxiv.math/0009052
openalex publication_date 2000/09/06 · arxiv created 2000/10/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The "similarity" degree of a unital operator algebra A was defined and studied in two recent papers of ours, where in particular we showed that it coincides with the "length" of an operator algebra. This paper brings several complements: we give direct proofs (with slight improvements) of several known facts on the length which were only known via the degree, and we show that the length of a type II1 factor with property Γ is at most 5, improving on a previous bound (≤ 44) due to E. Christensen.