Authors: | Bice, Tristan Farah, Ilijas |
Title: | Traces, ultrapowers and the pedersen-petersen C∗-algebras | Journal: | Houston Journal of Mathematics | Volume: | 41 | Issue: | 4 | First page: | 1175 | Last page: | 1190 | Issue Date: | 1-Jan-2015 | Rank: | M23 | ISSN: | 0362-1588 | Abstract: | Our motivating question was whether all traces on a U-ultrapower of a C∗-algebra A, where U is a non-principal ultrafilter on N, are necessarily U-limits of traces on A. We show that this is false so long as A has infinitely many extremal traces, and even exhibit a 22ℵ0 size family of such traces on the ultrapower. For this to fail even when A has finitely many traces implies that A contains operators that can be expressed as sums of n + 1 but not n∗-commutators, for arbitrarily large n. We show that this happens for a direct sum of Pedersen-Petersen C∗-algebras, and analyze some other interesting properties of these C-algebras. |
Keywords: | -Algebras | C | Commutators | Traces | Ultrapowers | Publisher: | University of Houston |
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