A Note on Z* algebras

Ali Taghavi

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arXiv · 1307.5836

A Note on Z* algebras

Ali Taghavi

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Abstract

We study some properies of $Z^{*}$ 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.

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Ali Taghavi. 2013-07-29. A Note on Z* algebras. https://arxiv.org/abs/1307.5836

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