The Order on Projections in C*-Algebras of Real Rank Zero

• Autorzy: Tristan Bice
• Języki publikacji: EN

Abstrakty

EN

We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of their lower bounds) decreasing sequences. Under the further assumption that the order is countably downwards closed, we show how to characterize greatest lower bounds of finite collections of projections, and their existence, using the norm and spectrum of simple product expressions of the projections in question. We also characterize the points at which the canonical homomorphism to the Calkin algebra preserves least upper bounds of countable collections of projections, namely that this occurs precisely when the span of the corresponding subspaces is closed.

Kategorie tematyczne

• 47A46: Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: 60
• Numer: 1
• Strony: 37-58

Daty

wydano

2012

Twórcy

autor

Tristan Bice

• Mathematical Logic Group, Kobe University, Kobe, Japan

Identyfikatory

DOI

10.4064/ba60-1-4