On the topological stable rank of non-selfadjoint operator algebras

2007/06/16 by K. R. Davidson, Kenneth R. Davidson, Davidson, K. R. +9
Computer Science · Mathematics · #19B10 #47A35 #47L75 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:19B10 #msc:47A35 #msc:47L75

paper · pdf · doi:10.48550/arxiv.0706.2447

14 pages

arxiv created 2007/06/16 · openalex publication_date 2007/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras, both the left and right topological stable ranks are infinite. We extend this latter result to Popescu's non-commutative disc algebras and to free semigroup algebras as well.

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