Angles in C*-algebras
Abstract
In this work we characterise the C*-algebras A generated by projections with the property that every pair of projections in A has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property is equivalent to a lattice theoretic property of projections and also to the property that the set of finite-dimensional *-subalgebras of A is directed.
Keywords
Cite
@article{arxiv.math/0601003,
title = {Angles in C*-algebras},
author = {M. Anoussis and A. Katavolos and I. G. Todorov},
journal= {arXiv preprint arXiv:math/0601003},
year = {2014}
}
Comments
The paper has been completely rewritten and differs essentially from "Lattices of projections and operator ranges in C*-algebras". New results have been added (Sec. 4 and 5) answering question 3.12 in the "Lattices..." paper. Sec. 4 of "Lattices ..." does not appear in the new version. Note that there is a gap in the proof of Theorem 4.10 of the old version