II1 Factors with non-isomorphic ultrapowers
Language
en
Article de revue
This item was published in
Duke Mathematical Journal. 2017
Duke University Press
English Abstract
We prove that there exist uncountably many separable II1 factors whose ultrapowers (with respect to arbitrary ultrafilters) are non-isomorphic. In fact, we prove that the families of non-isomorphic II1 factors originally ...Read more >
We prove that there exist uncountably many separable II1 factors whose ultrapowers (with respect to arbitrary ultrafilters) are non-isomorphic. In fact, we prove that the families of non-isomorphic II1 factors originally introduced by McDuff [MD69a, MD69b] are such examples. This entails the existence of a continuum of non-elementarily equivalent II1 factors, thus settling a well-known open problem in the continuous model theory of operator algebras.Read less <
Origin
Hal imported