Notes on automorphisms of ultrapowers of II₁ factors

David Sherman. "Notes on automorphisms of ultrapowers of II₁ factors." Studia Mathematica 195.3 (2009): 201-217. <http://eudml.org/doc/284770>.

@article{DavidSherman2009,
abstract = {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.},
author = {David Sherman},
journal = {Studia Mathematica},
keywords = {ultrapower; automorphisms; factors; approximately inner; outer automorphism},
language = {eng},
number = {3},
pages = {201-217},
title = {Notes on automorphisms of ultrapowers of II₁ factors},
url = {http://eudml.org/doc/284770},
volume = {195},
year = {2009},
}

TY - JOUR
AU - David Sherman
TI - Notes on automorphisms of ultrapowers of II₁ factors
JO - Studia Mathematica
PY - 2009
VL - 195
IS - 3
SP - 201
EP - 217
AB - 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.
LA - eng
KW - ultrapower; automorphisms; factors; approximately inner; outer automorphism
UR - http://eudml.org/doc/284770
ER -