On topological duality between non-unital commutative locally C*-algebras and locally k-spaces, and its applications.
by
Alexander A. Katz
Dep. of Math & CS, St. John's College of LAS, St. John's University, 300 Howard Ave., DaSilva 314, Staten Island, NY 10301, USA
Coauthors: Oleg Friedman, Dep. of Mathematical Sciences, University of South Africa, Pretoria, Republic of South Africa e-mail: friedman001@yahoo.com

We introduce a class of locally k-spaces- topological spaces, which are completely regular spaces, but more general then k-spaces, and use them to give a Gelfand-Naimark type topological duality theory between X and C₀(X), where X is a locally k-space, and C₀(X) is the algebra of all continuous functions on X vanishing at infinity. This theory, as an application, is further used to obtain an Arens-Kaplansky theorem and its inverse for commutative real non-unital locally C*-algebras.

Date received: December 25, 2009