Lists
Lists
Kissin, Edward, Shulman, Victor and Turovskii, Yuri (2024) Topological radicals, IX. Relations in ideals of C*-algebras. In: Special issue of Annals of Functional Analysis. Springer, London (UK). (In Press)
In this paper we pursue three aims.
The first one is to apply Amitsur’s relations and radicals theory to the study of the lattices IdA of closed two-sided ideals of C*-algebras A. We show that many new and many well-known results about C*-algebras follow naturally from this approach. To use ”relation-radical” approach, we consider various subclasses of the class A of all C*-algebras, which we call C*-properties, as they often linked to some properties of C*-algebras. We consider C*-properties P consisting of CCR- and of GCR-algebras; of C*-algebras with continuous trace; of real rank zero, AF, nuclear C*-algebras, etc. Each P defines reflexive relations≪P in all lattices IdA.
Our second aim is to determine the hierarchy and interconnection between properties in A.
Our third aim is to study the link between the radicals of relations ≪P in the lattices IdA and the topological radicals on A.
![[img]](/style/images/fileicons/text.png)
Restricted to Repository staff only until 31 December 2026.
Download (1MB)
 |
View Item |