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
Institute of Pure Mathematics, University of Tartu, 2 J. Liivi Street, Tartu 50409, Estonia
Received 4 November 2002
Copyright © 2003 Mati Abel and Olga Panova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.