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 |
Banach Algebra, Regular Norm, Normalized State, Spectral State
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| [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. |
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
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
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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Download@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}
}
TY - JOUR T1 - On the Paper: Numerical Radius Preserving Linear Maps on Banach Algebras AU - Mohammed El Azhari Y1 - 2017/10/10 PY - 2017 N1 - https://doi.org/10.11648/j.ml.20170305.11 DO - 10.11648/j.ml.20170305.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 50 EP - 51 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20170305.11 AB - 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. VL - 3 IS - 5 ER -
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