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 <kramer@mathematik.uni-wuerzburg.de> 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
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