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

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 Intrinsic Characterization of Real Locally C*- and Locally JB-Algebras

In the present paper we obtain an intrinsic characterization of real locally C*-algebras (projective limits of projective families of real C*-algebras) among complete real lmc *-algebras, and of locally JB-algebras (projective limits of projective families of JB-algebras) among complete fine Jordan locally multiplicatively-convex topological algebras.

A Note on Banach Principle for JW-algebras

In the sequel we establish the Banach Principle for semifinite JW-algebras without direct summand of type I sub 2, which extends the recent results of Chilin and Litvinov on the Banach Principle for semifinite von Neumann algebras to the case of JW-algebras.