Functiones et Approximatio Commentarii Mathematici

Algèbres de Jordan sans J-diviseurs topologiques généralisés de zéro

Abdelaziz Tajmouati and Ahmed Zinedine

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Abstract

Our aim in this paper is to show that the set $G_j(A)\cup \{0\}$, where $G_j(A)$ is the set of all J-invertible elements of a topological Jordan algebra $A$ without J-g.t.d.z, is isomorphic to $\mathbb{C}$ in the complex case. In the real case it is a $p$-normed quadratic J-division subalgebra of $A$. This result extends a well-known result of W. Żelazko ([11]) in the associative case to Jordan algebras.

Article information

Source
Funct. Approx. Comment. Math., Volume 61, Number 1 (2019), 47-55.

Dates
First available in Project Euclid: 26 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1540519335

Digital Object Identifier
doi:10.7169/facm/1744

Mathematical Reviews number (MathSciNet)
MR4012361

Subjects
Primary: 46H70: Nonassociative topological algebras [See also 46K70, 46L70]
Secondary: 17C60: Division algebras

Keywords
Jordan algebras Gelfand-Mazur theorem generalized topological J-divisors of zero

Citation

Zinedine, Ahmed; Tajmouati, Abdelaziz. Algèbres de Jordan sans J-diviseurs topologiques généralisés de zéro. Funct. Approx. Comment. Math. 61 (2019), no. 1, 47--55. doi:10.7169/facm/1744. https://projecteuclid.org/euclid.facm/1540519335


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References

  • [1] H. Arizmendi and W. Żelazko, A ${\cal B }_0$-algebra without generalized topological divisors of zero, Studia Math. 82 (1985), 191–198.
  • [2] S.J. Bhatt and S.H. Kulkarni, Gelfand-Mazur theorems in normed Algebras: A survey, Expo. Math (2017), http://dx.doi.org/10.1016/j.exmath.2017.08.004.
  • [3] M. Cabrera and Á. Rodríguez, On-associative normed algebras. Volume 1: The Vidav-Palmer and Gelfand-Naimark Theorems, Encyclopedia of Mathematics and Its Applications 154 (2014).
  • [4] M. Cabrera and Á. Rodríguez, On-associative normed algebras. Volume 2: Representation Theory and the Zel'manov Approach, Encyclopedia of Mathematics and Its Applications 167 (2018).
  • [5] N. El Yacoubi and H. Kemmoun, J-diviseurs topologiques de zéro dans les algèbres de Jordan p-normées unitaires, Periodica Mathematica Hungarica 35(3) (1997), 159–167.
  • [6] A.M. Kaidi, Bases para una teoria de las álgebras no associativas normadas, Tesis doctoral, Universidad de Granada (1977).
  • [7] H. Kemmoun, Théorèmes type Gelfand-Mazur et Kaplansky en théorie des algèbres non associatives, Thèse doctorale, Univ. Mohammed V, Rabat, (2000).
  • [8] M.E. Kuczma, On a problem of E. Michael concerning topological divisors of zero, Coll. Math. 19 (1968), 295–299.
  • [9] J.M. Moreno, Sobre álgebras de Jordan normadas completas, Tesis doctoral, Univ. de Granada, 149 (1977).
  • [10] W. Żelazko, Selected topics in topological algebras, Aarhus university, Lecture Notes 31 (1971).
  • [11] W. Żelazko, On generalized topological divisors of zero, Studia Math. 85 (1987) 137–148.