The Projection Calculus
Operator Algebras
2017-02-10 v3
Abstract
We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for C*-algebras of real rank zero, specifically on liftings, excising pure states and Kadison's transitivity theorem. Lastly, we investigate some order properties of the set of projections in C*-algebras of real rank zero, building on our previous work.
Cite
@article{arxiv.1203.3845,
title = {The Projection Calculus},
author = {Tristan Bice},
journal= {arXiv preprint arXiv:1203.3845},
year = {2017}
}