C*-algebras with approximate tracial oscillation zero

Huaxin Lin ֻ  (East China Normal University)

10:00-11:00, September 12, 2023   Science Building A503




Abstract:

A unital C*-algebra A has tracial approximate oscillation zero, if each positive element is approximated tracially by elements with small tracial oscillation. We show that if A has tracial approximate oscillation zero then A has stable rank one and the canonical map from the Cuntz semigroup of A to the corresponding affine function space is surjective. The converse also holds. As a by-product, we find that a separable simple C*-algebra which has almost stable rank one must have stable rank one, provided it has strict comparison and the canonical map is surjective.

About the speaker:

ֻ½ǹӴ֮һҪоC*-ࡣֽ90˾гδHalmos⣬2000Ժ벢չC*-𵽺õļۣ֤˼C*-ķඨ״λڼ򵥳ṹ㷺C*-࣬ƶC*-۵ķչ2014˺C*-ġElliott족ֽѧ׽ʿ2005ϺпѧһȽ1997ŷӴᡢ2014ѧҴᣨICMӴǻᱨ棬2015CBMSAMSNSFرʮϵн2018ѧҴ档2023׽ʻѧᣨInternational Congress of Basic Science, ICBS䷢ǰؿѧ

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