Notes on automorphisms of ultrapowers of II₁ factors

• Autorzy: David Sherman
• Języki publikacji: EN

Abstrakty

EN

In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II₁ factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is ℵ₀-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a separable nuclear C*-algebra into an ultrapower of a II₁ factor, equality of the induced traces implies unitary equivalence. All statements are proved using operator-algebraic techniques, but in the last section of the paper we indicate how the underlying principle is related to theorems of Henson's positive bounded logic.

Kategorie tematyczne

• 46M07: Ultraproducts
• 46L40: Automorphisms
• 46L10: General theory of von Neumann algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 195
• Numer: 3
• Strony: 201-217

Daty

wydano

2009

Twórcy

autor

David Sherman

• Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904, U.S.A.

Identyfikatory

DOI

10.4064/sm195-3-1