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

Tristan Bice. "The Order on Projections in C*-Algebras of Real Rank Zero." Bulletin of the Polish Academy of Sciences. Mathematics 60.1 (2012): 37-58. <http://eudml.org/doc/281285>.

@article{TristanBice2012,
abstract = {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.},
author = {Tristan Bice},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {-algebras; real rank zero; projections; order},
language = {eng},
number = {1},
pages = {37-58},
title = {The Order on Projections in C*-Algebras of Real Rank Zero},
url = {http://eudml.org/doc/281285},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Tristan Bice
TI - The Order on Projections in C*-Algebras of Real Rank Zero
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 1
SP - 37
EP - 58
AB - 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.
LA - eng
KW - -algebras; real rank zero; projections; order
UR - http://eudml.org/doc/281285
ER -