|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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