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On a Natural Ordering in Strictly Real Banach Algebras

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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.

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References

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

    M. A. Nejjari

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  1. M. A. Nejjari
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Correspondence to M. A. Nejjari.

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Nejjari, M.A. On a Natural Ordering in Strictly Real Banach Algebras. Mediterr. J. Math. 13, 2753–2758 (2016). https://doi.org/10.1007/s00009-015-0651-y

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  • DOI: https://doi.org/10.1007/s00009-015-0651-y

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