The relative commutant of separable C*-algebras of real rank zero
Ilijas Farah
TL;DR
This paper investigates whether the relative commutant of a separable C*-algebra in its ultrapower varies with different ultrafilters, addressing a question posed by Kirchberg.
Contribution
It provides an analysis of the dependence of the relative commutant on the ultrafilter choice for separable C*-algebras of real rank zero.
Findings
The relative commutant can depend on the ultrafilter in certain cases.
The paper characterizes conditions under which the relative commutant is independent of the ultrafilter.
Results contribute to understanding ultrapower constructions in operator algebras.
Abstract
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?
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Noncommutative and Quantum Gravity Theories