Monatshefte für Mathematik

, Volume 122, Issue 3, pp 205–213 | Cite as

Extension d'un théorème de Harte et applications aux algèbres de Jordan-Banach

  • Abdelaziz Maouche
Article

An extension of a theorem of Harte and applications to Jordan-Banach algebras

Abstract

In this paper we study some questions related to spectral theory in Jordan-Banach algebras. Firstly, we introduce the notion of exponential spectrum and then we extend to Jordan-Banach algebras a theorem due to Robin Harte in the associative case. Secondly, these results are used to get a theorem on spectral perturbation by inessential elements in Jordan-Banach algebras.

1991 Mathematics Subject Classification

46 H 70 (17 A 15) 

Key words

Jordan-Banach algebra Exponential spectrum Inessential ideal 

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References

  1. [1]
    Aupetit, B.: A Primer on Spectral Theory. New York: Springer. 1991.Google Scholar
  2. [2]
    Benslimane, M., Rodríguez Palacios, A.: Caractérisation spectrale des algèbres de Jordan-Banach non commutatives complexes modulaires annihilatrices. J. Algebra140, 344–354 (1991).Google Scholar
  3. [3]
    Harte, R.: Spectral mapping theorems. Proc. Roy Irish. Acad. Sect. A72, 89–107 (1972).Google Scholar
  4. [4]
    Hogben, L., Mccrimmon, K.: Maximal modular inner ideals and the Jacobson radical of a Jordan algebra. J. Algebra68, 155–169 (1981).Google Scholar
  5. [5]
    Jacobson, N.: Structure Theory of Jordan Algebras. Lecture Notes 5. The University of Arkansas, Fayetteville 1981.Google Scholar
  6. [6]
    Loos, O.: On the set of invertible elements in Banach-Jordan algebras. Preprint.Google Scholar
  7. [7]
    Loos, O.: Properly algebraic and spectrum-finite ideals in Jordan Systems. Math. Proc. Camb. Phil. Soc.114, 149–161 (1993).Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Abdelaziz Maouche
    • 1
  1. 1.Département de mathématiques et statistiqueUniversité LavalSte-FoyCanada

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