Authors: | Farah, Ilijas | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | All automorphisms of the Calkin algebra are inner | Journal: | Annals of Mathematics | Volume: | 173 | Issue: | 2 | First page: | 619 | Last page: | 661 | Issue Date: | 1-Mar-2011 | Rank: | M21a | ISSN: | 0003-486X | DOI: | 10.4007/annals.2011.173.2.1 | Abstract: | We prove that it is relatively consistent with the usual axioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips-Weaver construction of an outer automorphism using the Continuum Hypothesis, this gives a complete solution to a 1977 problem of Brown-Douglas-Fillmore. We also give a simpler and self-contained proof of the Phillips-Weaver result. |
Keywords: | Calkin algebra | Continuum Hypothesis | Todorcevic's axiom | approximate homomorphisms | independence results | outer automorphisms | Publisher: | Princeton University & Institute for Advanced Study |
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