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Mediterranean Journal of Mathematics

, Volume 13, Issue 5, pp 2753–2758 | Cite as

On a Natural Ordering in Strictly Real Banach Algebras

  • M. A. Nejjari
Article
  • 48 Downloads

Abstract

We show that in a real Banach algebra the connected component of the group of invertible elements containing the unit can not be convex cone except when the algebra is strictly real. We also get that in a strictly real Banach algebra containing no zero divisors any invertible element is either positive or negative.

Mathematics Subject Classification

Primary 46H05 Secondary 46K05 

Keywords

Real algebras convex cone positive elements zero-divisors 

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References

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Centre régional des metiers de l’éducation et de la formation (CRMEF)OujdaMorocco

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