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The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra

Received: 10 January 2015     Accepted: 25 January 2015     Published: 11 February 2015
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Abstract

Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 2)
DOI 10.11648/j.pamj.20150402.12
Page(s) 43-46
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), 2015. Published by Science Publishing Group

Keywords

*-Algebra, *Prime Algebra, *-Simple Algebra, Automatic Continuity, Separting Space

References
[1] F.F. Bonsall and J. Duncan, Complete normed algebras, Spring6 Verlag. Berlin (1973).
[2] J. Cusack, Automatic Continuity and topologically simple Banach algebras, J. London. Math. Soc (2), 16 (1977), 439-500.
[3] R. V. Garimella, Continuity of derivation on some semi-prime Banach algebra, Proc. Amer. Math. Soc., 99 (1987), 289 [12]-292.
[4] R.V. Garimella, Prime ideals and the continuity of derivation on integral domins, Indian. J. Pure app. Math, 22 (12) (1991), 1013-1018.
[5] R.V. Garimella, On nilpotenty of the separting ideal of a derivation. Proc. Amer. Math. Soc., 117, (1993), 167-174.
[6] N. Jacobson, Basic Algebra II, W. H. Ferman and Compagny (1980).
[7] B.E Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73, (1967) 537-539
[8] B.E Johnson, and A. M. Sinclair, Continuity of derivation and a problem of Kaplansky, Amer. J. Math. Math. 90 (1968), 1067-1073.
[9] M. Mathieu et V. Runde, Derivations mapping into the radical II, Bull. London Math. Soc., 24(1992), 485-487.
[10] V. Runde, Continuity of derivations and epimorphisms, Pacific J. of Math., Vol. 147, Nr. 2 (1991), 365-374.
[11] A. M. Sinclair, Automatic Continuity of linear operators, London. Math. Soc. Lecture Note Series 21 (C.U.P., Combridge 1976).
[12] Y. TIDLI, L. OUKHTITE, A. TAJMOUATI, On the Automatic continuity of the epimorphisms in *algebras of Banach. IJMMS 2004: 22 1183-1187 (2002).
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  • APA Style

    Youssef Tidli. (2015). The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra. Pure and Applied Mathematics Journal, 4(2), 43-46. https://doi.org/10.11648/j.pamj.20150402.12

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    ACS Style

    Youssef Tidli. The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra. Pure Appl. Math. J. 2015, 4(2), 43-46. doi: 10.11648/j.pamj.20150402.12

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    AMA Style

    Youssef Tidli. The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra. Pure Appl Math J. 2015;4(2):43-46. doi: 10.11648/j.pamj.20150402.12

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  • @article{10.11648/j.pamj.20150402.12,
      author = {Youssef Tidli},
      title = {The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {2},
      pages = {43-46},
      doi = {10.11648/j.pamj.20150402.12},
      url = {https://doi.org/10.11648/j.pamj.20150402.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150402.12},
      abstract = {Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.},
     year = {2015}
    }
    

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Author Information
  • Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Marhaz, Fes, Morroco

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