Authors: | Farah, Ilijas Hirshberg, Ilan Vignati, Alessandro |
Title: | The Calkin algebra is ℵ1 -universal | Journal: | Israel Journal of Mathematics | Volume: | 237 | First page: | 287 | Last page: | 309 | Issue Date: | 1-Mar-2020 | Rank: | M22 | ISSN: | 0021-2172 | DOI: | 10.1007/s11856-020-2007-y | Abstract: | We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character ℵ1 embed into the Calkin algebra, Q(H). Together with other results, this shows that each of the following assertions is relatively consistent with ZFC: (i) Q(H) is a 2ℵ0-universal C*-algebra. (ii) There exists a 2ℵ0-universal C*-algebra, but Q(H) is not 2ℵ0-universal, (iii) A 2ℵ0-universal C*-algebra does not exist. We also prove that it is relatively consistent with ZFC that (iv) there is no ℵ1-universal nuclear C*-algebra, and that (v) there is no ℵ1-universal simple nuclear C*-algebra. |
Publisher: | Springer Link |
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