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Year 2018, , 121 - 124, 26.06.2018
https://doi.org/10.32323/ujma.399537

Abstract

References

  • [1] Aupetit Bernard, A Primer on spectral theory, Universitext, Springer, New York, 1991.
  • [2] Aupetit Bernard, “Spectral characterisation of the radical in Banach and Jordan-Banach algebras”, Math. Proc. Camb. Philos. Soc. 114 (1993), 31-35.
  • [3] Aupetit Bernard, “Spectrum-preserving linear mappings between Banach algebras and Jordan-Banach algebras”, J. London Math. Soc. 262 (2000), 917-924.
  • [4] Aupetit Bernard and Abdelaziz Maouche, “Trace and determinant in Jordan-Banach algebras”, Publ. Mat. 46 (2002), 3-16.
  • [5] Braatvedt , G., Brits, R., and Raubeuheimer, H., “Spectral characterization of scalars in a Banach algebra”, Bull. London Math. Soc. 41 (2009), 1095-1104.
  • [6] Miguel Cabrera Garcia and Angel Rodriguez Palacios, Non-Associative Normed Algebras, Encyclopedia of Mathematics and its Applications 154, Cambridge, 1994.
  • [7] O. Loos, “On the set of invertible elements in Banach-Jordan algebras”, Results in Math. 29 (1996), no. 1-2, 111-114.
  • [8] Kevin McCrimmon, A Taste of Jordan algebras, Universitext, Springer, New York, 2004.
  • [9] Abdelaziz Maouche, “Diagonalization in Jordan-Banach algebras”, Extracta Mathematicae. Vol. 19, Num. 2 (2004), 257-260.
  • [10] K.A. Zhevlakov, A.M. Slin’ko, I.P. Shestakov and A. I. Shirshov, Rings that are nearly associative, Academic Press, New York, 1982.

Scalar characterization in Banach Jordan algebras

Year 2018, , 121 - 124, 26.06.2018
https://doi.org/10.32323/ujma.399537

Abstract

Using a Diagonalization Theorem obtained when the spectrum is Lipschitzian, we extend a result of G. Braatvedt on scalar characterization in Banach algebras to Banach-Jordan algebras. We also establish that any element of a semisimple Banach-Jordan algebra with the property that all elements in some neighbourhood of the identity are spectrally invariant under multiplication by the quadratic U operator, has analogs with the identity.

References

  • [1] Aupetit Bernard, A Primer on spectral theory, Universitext, Springer, New York, 1991.
  • [2] Aupetit Bernard, “Spectral characterisation of the radical in Banach and Jordan-Banach algebras”, Math. Proc. Camb. Philos. Soc. 114 (1993), 31-35.
  • [3] Aupetit Bernard, “Spectrum-preserving linear mappings between Banach algebras and Jordan-Banach algebras”, J. London Math. Soc. 262 (2000), 917-924.
  • [4] Aupetit Bernard and Abdelaziz Maouche, “Trace and determinant in Jordan-Banach algebras”, Publ. Mat. 46 (2002), 3-16.
  • [5] Braatvedt , G., Brits, R., and Raubeuheimer, H., “Spectral characterization of scalars in a Banach algebra”, Bull. London Math. Soc. 41 (2009), 1095-1104.
  • [6] Miguel Cabrera Garcia and Angel Rodriguez Palacios, Non-Associative Normed Algebras, Encyclopedia of Mathematics and its Applications 154, Cambridge, 1994.
  • [7] O. Loos, “On the set of invertible elements in Banach-Jordan algebras”, Results in Math. 29 (1996), no. 1-2, 111-114.
  • [8] Kevin McCrimmon, A Taste of Jordan algebras, Universitext, Springer, New York, 2004.
  • [9] Abdelaziz Maouche, “Diagonalization in Jordan-Banach algebras”, Extracta Mathematicae. Vol. 19, Num. 2 (2004), 257-260.
  • [10] K.A. Zhevlakov, A.M. Slin’ko, I.P. Shestakov and A. I. Shirshov, Rings that are nearly associative, Academic Press, New York, 1982.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Abdelaziz Maouche

Publication Date June 26, 2018
Submission Date February 28, 2018
Acceptance Date April 6, 2018
Published in Issue Year 2018

Cite

APA Maouche, A. (2018). Scalar characterization in Banach Jordan algebras. Universal Journal of Mathematics and Applications, 1(2), 121-124. https://doi.org/10.32323/ujma.399537
AMA Maouche A. Scalar characterization in Banach Jordan algebras. Univ. J. Math. Appl. June 2018;1(2):121-124. doi:10.32323/ujma.399537
Chicago Maouche, Abdelaziz. “Scalar Characterization in Banach Jordan Algebras”. Universal Journal of Mathematics and Applications 1, no. 2 (June 2018): 121-24. https://doi.org/10.32323/ujma.399537.
EndNote Maouche A (June 1, 2018) Scalar characterization in Banach Jordan algebras. Universal Journal of Mathematics and Applications 1 2 121–124.
IEEE A. Maouche, “Scalar characterization in Banach Jordan algebras”, Univ. J. Math. Appl., vol. 1, no. 2, pp. 121–124, 2018, doi: 10.32323/ujma.399537.
ISNAD Maouche, Abdelaziz. “Scalar Characterization in Banach Jordan Algebras”. Universal Journal of Mathematics and Applications 1/2 (June 2018), 121-124. https://doi.org/10.32323/ujma.399537.
JAMA Maouche A. Scalar characterization in Banach Jordan algebras. Univ. J. Math. Appl. 2018;1:121–124.
MLA Maouche, Abdelaziz. “Scalar Characterization in Banach Jordan Algebras”. Universal Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 121-4, doi:10.32323/ujma.399537.
Vancouver Maouche A. Scalar characterization in Banach Jordan algebras. Univ. J. Math. Appl. 2018;1(2):121-4.

Cited By

Commutable Matrix-Valued Functions and Operator-Valued Functions
Communications in Advanced Mathematical Sciences
Abdelaziz MAOUCHE
https://doi.org/10.33434/cams.759336

 23181

Universal Journal of Mathematics and Applications 

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