74 citations · 433 across the 68 of their papers we have counts for
7 papers · 2 filters
Existentially closed II_1 factors
Ilijas Farah, Isaac Goldbring, Bradd Hart +1
We examine the properties of existentially closed (R^omega-embeddable) II_1 factors. In particular, we use the fact that every automorphism of an existentially closed (R^omega-embe…
A nonseparable amenable operator algebra which is not isomorphic to a C*-algebra
Yemon Choi, Ilijas Farah, Narutaka Ozawa
It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample.…
Traces, Ultrapowers and the Pedersen-Petersen C*-Algebras
Tristan Bice, Ilijas Farah
Our motivating question was whether all traces on a U-ultrapower of a C*-algebra A, where U is a non-principal ultrafilter on N, are necessarily U-limits of traces on A. We show th…
The isomorphism relation for separable C*-algebras
George A. Elliott, Ilijas Farah, Vern Paulsen +3
We prove that the isomorphism relation for separable C-algebras, and also the relations of complete and -isometry for operator spaces and systems, are Borel reducible to the…
Amalgamating R^ω-embeddable von Neumann algebras
Ilijas Farah, Isaac Goldbring, Bradd Hart
We observe how a classical model-theoretic fact proves the existence of many strong amalgamation bases for the class of R^ω-embeddable von Neumann algebras, where R is the hyperfin…
Nonseparable UHF algebras II: Classification
Ilijas Farah, Takeshi Katsura
For every uncountable cardinal there are nonisomorphic simple AF algebras of density character and nonisomorphic hyperfinite II factors of density character…