International Journal of Nonlinear Analysis and Applications

Linear maps which are local (g, h)-ternary derivations from ∗-module extension Banach algebras into their periodical duals

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

2 Department of Mathematics, College of Education for Pure Science, University of Mosul, Mosul, Iraq

Abstract

We introduce a $\ast$-module extension Banach algebras to generalized the results of Niazi and Miri. Precisely, every local $(g,h)$-ternary derivation from a $\ast$-module extension Banach algebra into one of its periodical duals is $(g,h)$-ternary derivation.

Keywords

[1] N. Arga¸c, A. Kaya, and A. Kisir, (σ, τ )-derivations in prime rings, Mat. J. Okayama Univer. 29 (1987), no. 1, 173–177.
[2] S. Ayupov, K. Kudaybergenov, and A.M. Peralta, A survey on local and 2-local derivations on C*-and von Neumann algebras, Topics in Functional Analysis and Algebra”, Contemp. Math 672 (2016), 73–126.
[3] M. Burgos, F.J. Fern´andez-Polo, J.J. Garc´es, and A.M. Peralta, Local triple derivations on C*-algebras, Commun. Algebra 42 (2014), no. 3, 1276–1286.
[4] M. Burgos, F.J. Fern´andez-Polo, and A.M. Peralta, Local triple derivations on C*-algebras and JB*-triples, Bull. London Math. Soc. 46 (2014), no. 4, 709–724.
[5] S. Goldstein, Stationarity of operator algebras, J. Funct. Anal. 118 (1993), no. 2, 275–308.
[6] B. E. Johnson, Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. Proc. Camb. Phil. Soc., vol. 120, Cambridge University Press, 1996, pp. 455–473.
[7] J. Li and Z. Pan, Annihilator-preserving maps, multipliers, and derivations , Linear Algebra Appl. 432 (2010), no. 1, 5–13.
[8] M. Mackey, Local derivations on Jordan triples, Bull. London Math. Soc. 45 (2013), no. 4, 811–824.
[9] A.R. Medghalchi and H. Pourmahmood-Aghababa, The first cohomology group of module extension banach algebras, Rocky Mount. J. Math. (2011), 1639–1651.
[10] M. Niazi and M.R. Miri, Local triple derivations from C*-algebras into their iterated duals , Tamkang J. Math. 49 (2018), no. 2, 99–113.
[11] Y. Zhang, Weak amenability of module extensions of banach algebras, Trans. Amer. Math. Soc. 354 (2002), no. 10, 4131–4151.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 5
May 2023
Pages 211-217
  • Receive Date: 12 January 2023
  • Revise Date: 08 March 2023
  • Accept Date: 30 March 2023