Cuntz semigroups of C*-algebras of stable rank one and projective Hilbert modules

2010/01/26 by Huaxin Lin, Lin, Huaxin · 3 citations
Mathematics · #46l05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46l05

paper · pdf · doi:10.48550/arxiv.1001.4558

The title has been changed.

openalex publication_date 2010/01/26 · arxiv created 2010/05/11 · arxiv updated 2010/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let A be a simple C*-algebra of stable rank one and let p and q be two σ-compact open projections. It is proved that there is a continuous path of unitaries in A which connects open sub-projections of p which is compactly contained in p to those in q. It is also shown that every Hilbert module is projective in the category whose morphisms are bounded module maps with adjoints. A discussion of projective Hilbert modules (whose morphisms are bounded module maps) is also given.

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• The corona algebra of stablized Jiang-Su algebra
• On classification of simple non-unital amenable C*-algebras, II
• The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension

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