International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 40, Pages 2541-2552
doi:10.1155/S0161171203211066

Real Gel'fand-Mazur division algebras

Mati Abel and Olga Panova

Institute of Pure Mathematics, University of Tartu, 2 J. Liivi Street, Tartu 50409, Estonia

Abstract

We show that the complexification (A˜,τ˜) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification (A˜,τ˜) of a commutative real exponentially galbed algebra (A,τ) with bounded elements are bounded if the multiplication in (A,τ) is jointly continuous. We give conditions for a commutative strictly real topological division algebra to be a commutative real Gel'fand-Mazur division algebra.