English

A Note on Z* algebras

Operator Algebras 2013-07-30 v2

Abstract

We study some properies of ZZ^{*} 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}
}
R2 v1 2026-06-22T00:55:44.101Z