A Note on Z* algebras
Operator Algebras
2013-07-30 v2
Abstract
We study some properies of algebras, thos C^* algebra which all positive elements are zero divisors. We show by means of an example that an extension of a Z* algebra by a Z* algebra is not necessarily Z* algebra. However we prove that an extension of a non Z* algebra by a non Z* algebra is again a Z^* algebra. As an application of our methods, we prove that evey compact subset of the positive cones of a C* algebra has an upper bound in the algebra.
Keywords
Cite
@article{arxiv.1307.5836,
title = {A Note on Z* algebras},
author = {Ali Taghavi},
journal= {arXiv preprint arXiv:1307.5836},
year = {2013}
}