International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 40, Pages 2541-2552
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.
We show that the complexification of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification of a commutative real exponentially galbed algebra with bounded elements are bounded if the multiplication in is jointly continuous. We give conditions for a commutative strictly real topological division algebra to be a commutative real Gel'fand-Mazur division algebra.