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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