Real Gel'fand-Mazur division algebras

Mati Abel and Olga Panova

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-12

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:389796

DOI: 10.1155/S0161171203211066

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