From: israel@math.ubc.ca (Robert Israel) Newsgroups: sci.math.research Subject: Re: Banach skew fields or near fields Date: 30 May 1998 00:46:12 GMT In article <356D115A.4CDF3ECD@mathematik.uni-wuerzburg.de>, Linus Kramer writes: |> I have a question on infinite dimensional (real) Banach algebras |> (with unit 1). |> |> Can such a Banach algebra be a skew field ( = associative division |> ring) or a division algebra (not necessarily associative, every ??? by definition, a Banach algebra is associative. |> element invertibel)? Any Banach division algebra is isomorphic to either the reals, complexes or quaternions: see Rickart, General Theory of Banach Algebras, Theorem 1.7.6. Robert Israel israel@math.ubc.ca Department of Mathematics (604) 822-3629 University of British Columbia fax 822-6074 Vancouver, BC, Canada V6T 1Z2