146 research outputs found
The relative commutant of separable C*-algebras of real rank zero
We answer a question of E. Kirchberg (personal communication): does the
relative commutant of a separable C*-algebra in its ultrapower depend on the
choice of the ultrafilter?Comment: To appear in Journal of Functional Analysi
Logic and operator algebras
The most recent wave of applications of logic to operator algebras is a young
and rapidly developing field. This is a snapshot of the current state of the
art.Comment: A minor chang
Automorphisms of corona algebras, and group cohomology
In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis,
there exists an outer automorphism of the Calkin algebra. (The Calkin algebra
is the algebra of bounded operators on a separable complex Hilbert space,
modulo the compact operators.) In this paper we establish that the analogous
conclusion holds for a broad family of quotient algebras. Specifically, we will
show that assuming the Continuum Hypothesis, if is a separable algebra
which is either simple or stable, then the corona of has nontrivial
automorphisms. We also discuss a connection with cohomology theory, namely,
that our proof can be viewed as a computation of the cardinality of a
particular derived inverse limit
- …