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On the Paper: Numerical Radius Preserving Linear Maps on Banach Algebras

Received: 16 May 2017     Accepted: 8 September 2017     Published: 10 October 2017
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Abstract

We give an example of a unital commutative complex Banach algebra having a normalized state which is not a spectral state and admitting an extreme normalized state which is not multiplicative. This disproves two results by Golfarshchi and Khalilzadeh.

Published in Mathematics Letters (Volume 3, Issue 5)
DOI 10.11648/j.ml.20170305.11
Page(s) 50-51
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Banach Algebra, Regular Norm, Normalized State, Spectral State

References
[1] F. F. Bonsall and J. Duncan, Complete normed algebras, New York: Springer Verlag 1973.
[2] A. K. Gaur and T. Husain, Spatial numerical ranges of elements of Banach algebras, International Journal of Mathematics and Mathematical Sciences, 12(4)(1989), 633-640.
[3] A. K. Gaur and Z. V. Kovářík, Norms, states and numerical ranges on direct sums, Analysis, 11(2-3)(1991), 155-164.
[4] F. Golfarshchi and A. A. Khalilzadeh, Numerical radius preserving linear maps on Banach algebras, International Journal of Pure and Applied Mathematics, 88(2)(2013), 233-238.
[5] A. Orenstein, Regular norm and the operator seminorm on a non-unital complex commutative Banach algebra, arXiv: 1410.8790v2 [math.FA] 11 Dec 2015.
[6] C. E. Rickart, General theory of Banach algebras, New York: Van Nostrand 1960.
Cite This Article
  • APA Style

    Mohammed El Azhari. (2017). On the Paper: Numerical Radius Preserving Linear Maps on Banach Algebras. Mathematics Letters, 3(5), 50-51. https://doi.org/10.11648/j.ml.20170305.11

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    ACS Style

    Mohammed El Azhari. On the Paper: Numerical Radius Preserving Linear Maps on Banach Algebras. Math. Lett. 2017, 3(5), 50-51. doi: 10.11648/j.ml.20170305.11

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    AMA Style

    Mohammed El Azhari. On the Paper: Numerical Radius Preserving Linear Maps on Banach Algebras. Math Lett. 2017;3(5):50-51. doi: 10.11648/j.ml.20170305.11

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  • @article{10.11648/j.ml.20170305.11,
      author = {Mohammed El Azhari},
      title = {On the Paper: Numerical Radius Preserving Linear Maps on Banach Algebras},
      journal = {Mathematics Letters},
      volume = {3},
      number = {5},
      pages = {50-51},
      doi = {10.11648/j.ml.20170305.11},
      url = {https://doi.org/10.11648/j.ml.20170305.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20170305.11},
      abstract = {We give an example of a unital commutative complex Banach algebra having a normalized state which is not a spectral state and admitting an extreme normalized state which is not multiplicative. This disproves two results by Golfarshchi and Khalilzadeh.},
     year = {2017}
    }
    

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Author Information
  • Department of Mathematics, Ecole Normale Supérieure, Rabat, Morocco

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