ALL AUTOMORPHISMS OF THE CALKIN ALGEBRA ARE INNER

By Ilijas Farah. 2007

112 citations recorded by the source corpus.

We prove that it is relatively consistent with the usual ax- ioms 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3475715e424894ad9dc680610853f61b20ca8c6b

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Model theory of operator algebras II: model theory (2010, background): “The main result of [9] implies that if ZFC is consistent then there is a model of ZFC in which there is no such automorphism.”
On the consistency strength of the proper forcing axiom (2010, background): “sis problem for uncountable linear orders [15]. Even problems originating from other ﬁelds of mathematics and apparently unrelated to set theory have been settled appealing to PFA. For example, Farah [3] recently proved the nonexistence of outer automorphisms of the Calkin algebra assuming PFA. The ”
ALMOST SOLUTIONS OF EQUATIONS IN PERMUTATIONS (2007, background): “(Calkin algebras, essentially normal operators, see [4] and the bibliography in it.”