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Abstract: In functional analysis, approximative properties of an object become precisein its ultrapower. We discuss this idea and its consequences for automorphismsof II 1 factors. Here are some sample results: 1 an automorphism isapproximately inner if and only if its ultrapower is aleph 0-locally inner; 2the ultrapower of an outer automorphism is always outer; 3 for unital*-homomorphisms from a separable nuclear C*-algebra into an ultrapower of aII 1 factor, equality of the induced traces implies unitary equivalence. Allstatements are proved using operator algebraic techniques, but in the lastsection of the paper we indicate how the underlying principle is related totheorems of Henson-s positive bounded logic.



Author: David Sherman

Source: https://arxiv.org/







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