On Bounded Approximate Identities and Existence of Dense Ideals in Real Locally C*- and Locally JB-Algebras

Alexander A. Katz; Oleg Friedman

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arxiv 0809.0306 v1 pith:X6SKGAPY submitted 2008-09-01 math.OA math.FA

On Bounded Approximate Identities and Existence of Dense Ideals in Real Locally C*- and Locally JB-Algebras

Alexander A. Katz , Oleg Friedman This is my paper

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It has been established by Inoue that a complex locally C*-algebra with a dense ideal posesses a bounded approximate identity which belonges to that ideal. It has been shown by Fritzsche that if a unital complex locally C*-algebra has an unbounded element then it also has a dense one-sided ideal. In the present paper we obtain analogues of the aforementioned results of Inoue and Fritzsche for real locally C*-algebras (projective limits of projective families of real C*-algebras), and for locally JB-algebras (projective limits of projective families of JB-algebras).

On Bounded Approximate Identities and Existence of Dense Ideals in Real Locally C*- and Locally JB-Algebras

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