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

TL;DR

This paper provides an intrinsic characterization of real locally C*-algebras and locally JB-algebras within the framework of complete real locally multiplicatively-convex topological algebras, expanding understanding of their structure.

Contribution

It introduces a new intrinsic characterization of these algebras among complete real lmc *-algebras and Jordan locally multiplicatively-convex algebras, respectively.

Findings

Characterization of real locally C*-algebras as projective limits of real C*-algebras.

Characterization of locally JB-algebras as projective limits of JB-algebras.

Provides a structural framework for analyzing these classes of algebras.

Abstract

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.