All automorphisms of the Calkin algebra are inner

• 成果类型: Article
• 署名作者: Farah, Ilijas
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.2.1
• 发表日期: 2011
• 页码: 619-661
• 关键词: strong homology; EXTENSIONS

摘要

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 prolem of Brown-Douglas-Fillmore. We also give a simpler and self-contained proof of the Phillips-Weaver result.