Cuntz semigroups of ultraproduct C*-algebras

Autor:	Antoine, Ramon, Perera, Francesc, Thiel, Hannes
Rok vydání:	2019
Předmět:	Mathematics - Operator Algebras 06B35 06F05 46L05 46M07 (Primary) 03C20 06B30 18A30 18A35 18B35 19K14 46M15 46M40 (Secondary)
Druh dokumentu:	Working Paper
DOI:	10.1112/jlms.12343
Popis:	We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C*-algebras agrees with the (ultra)product of the scaled Cuntz semigroups of the involved C*-algebras. As applications of our results, we compute the non-stable K-Theory of general (ultra)products of C*-algebras and we characterize when ultraproducts are simple. We also give criteria that determine order properties of these objects, such as almost unperforation. Comment: 34 pages; to appear in Journal of the London Mathematical Society
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.03208 Zobrazit plný text záznamu View this record from Arxiv