On a Local Structure in Kaplansky Algebras. Definitions and Basic Properties
Operator Algebras
2010-12-24 v1 Functional Analysis
Abstract
We introduce and study locally AW*-algebras (Baer locally C*-algebras) as a locally multiplicatively-convex generalization of AW*-algebras of Kaplansky. Among other basic properties of these algebras, it is established that: {\bullet} A locally C*-algebra is a locally AW*-algebra iff there exists its Arens-Michael decomposition consisting entirely of AW*-algebras; {\bullet} A bounded part of a locally AW*-algebra is an AW*-algebra; {\bullet} The Spectral Theorem for locally AW*-algebras.
Keywords
Cite
@article{arxiv.1012.5196,
title = {On a Local Structure in Kaplansky Algebras. Definitions and Basic Properties},
author = {Alexander A. Katz},
journal= {arXiv preprint arXiv:1012.5196},
year = {2010}
}