The second dual of strongly zero-product preserving maps

Document Type : Research Paper

Author

Faculty of Mathematical Sciences‎, ‎Shahrood University of Technology‎, ‎P.O‎. ‎Box 3619995161-316‎, ‎Shahrood‎, ‎Iran.

Abstract

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are defined. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of a strongly zero-product, strongly Jordan zero-product and strongly Lie zero-product preserving map on a certain class of normed algebras are investigated.

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References

M.A. Chebotar, W.-F. Ke, P.-H. Lee and N.-C. Wong, Mappings preserving zero products, Studia Math. 155 (2003), no. 1, 77--94.
H. Ghahramani, Zero product determined triangular algebras, Linear Multilinear Algebra 61 (2013) 741--757.
A.R. Khoddami, On maps preserving strongly zero-products, Chamchuri J. Math. 7 (2015) 16--23.
A.R. Khoddami, Strongly zero-product preserving maps on normed algebras induced by a bounded linear functional, Khayyam J. Math. 1 (2015), no. 1, 107--114.
A.R. Khoddami, On strongly Jordan zero-product preserving maps, Sahand Commun Math. Anal. 3 (2016), no. 1, 53--61.
A.R. Khoddami and H.R. Ebrahimi Vishki, The higher duals of a Banach algebra induced by a bounded linear functional, Bull. Math. Anal. Appl. 3 (2011) 118--122.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 6
November 2017
Pages 1781-1790

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History

  • Receive Date: 28 February 2016
  • Revise Date: 10 October 2016
  • Accept Date: 15 October 2016

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